[Convergence des interfaces dʼIsing vers les courbes SLE introduites par Schramm]
We show how to combine our earlier results to deduce strong convergence of the interfaces in the planar critical Ising model and its random-cluster representation to Schrammʼs SLE curves with parameters
Cet article explique comment combiner certains résultats antérieurs des différents auteurs afin de montrer la convergence forte des interfaces du modèle dʼIsing critique planaire et de sa représentation FK vers les courbes
Accepté le :
Publié le :
Dmitry Chelkak 1, 2 ; Hugo Duminil-Copin 3 ; Clément Hongler 4 ; Antti Kemppainen 5 ; Stanislav Smirnov 1, 3
@article{CRMATH_2014__352_2_157_0, author = {Dmitry Chelkak and Hugo Duminil-Copin and Cl\'ement Hongler and Antti Kemppainen and Stanislav Smirnov}, title = {Convergence of {Ising} interfaces to {Schramm's} {SLE} curves}, journal = {Comptes Rendus. Math\'ematique}, pages = {157--161}, publisher = {Elsevier}, volume = {352}, number = {2}, year = {2014}, doi = {10.1016/j.crma.2013.12.002}, language = {en}, }
TY - JOUR AU - Dmitry Chelkak AU - Hugo Duminil-Copin AU - Clément Hongler AU - Antti Kemppainen AU - Stanislav Smirnov TI - Convergence of Ising interfaces to Schrammʼs SLE curves JO - Comptes Rendus. Mathématique PY - 2014 SP - 157 EP - 161 VL - 352 IS - 2 PB - Elsevier DO - 10.1016/j.crma.2013.12.002 LA - en ID - CRMATH_2014__352_2_157_0 ER -
%0 Journal Article %A Dmitry Chelkak %A Hugo Duminil-Copin %A Clément Hongler %A Antti Kemppainen %A Stanislav Smirnov %T Convergence of Ising interfaces to Schrammʼs SLE curves %J Comptes Rendus. Mathématique %D 2014 %P 157-161 %V 352 %N 2 %I Elsevier %R 10.1016/j.crma.2013.12.002 %G en %F CRMATH_2014__352_2_157_0
Dmitry Chelkak; Hugo Duminil-Copin; Clément Hongler; Antti Kemppainen; Stanislav Smirnov. Convergence of Ising interfaces to Schrammʼs SLE curves. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 157-161. doi : 10.1016/j.crma.2013.12.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.002/
[1] Hölder regularity and dimension bounds for random curves, Duke Math. J., Volume 99 (1999) no. 3, pp. 419-453
[2] Infinite conformal symmetry of critical fluctuations in two dimensions, J. Stat. Phys., Volume 34 (1984) no. 5–6, pp. 763-774
[3] Robust discrete complex analysis: a toolbox, 2012 (Preprint) | arXiv
[4] D. Chelkak, H. Duminil-Copin, Clément Hongler, Crossing probabilities in topological rectangles for the critical planar FK Ising model, Preprint, , 2013. | arXiv
[5] Conformal invariance of spin correlations in the planar Ising model, 2012 (Preprint) | arXiv
[6] Holomorphic spinor observables in the critical Ising model, Commun. Math. Phys., Volume 322 (2013) no. 2, pp. 303-332
[7] Universality in the 2D Ising model and conformal invariance of fermionic observables, Invent. Math., Volume 189 (2012) no. 3, pp. 515-580
[8] Connection probabilities and RSW-type bounds for the two-dimensional FK Ising model, Commun. Pure Appl. Math., Volume 64 (2011) no. 9, pp. 1165-1198
[9] Conformal invariance of lattice models, Probability and Statistical Physics in Two and More Dimensions, Clay Math. Proc., vol. 15, Amer. Math. Soc., Providence, RI, 2012, pp. 213-276
[10] Conformal invariance of Ising model correlations, 2010 (PhD thesis)
[11] The energy density in the planar Ising model, Acta. Math., Volume 211 (2013) no. 2, pp. 191-225
[12] Random curves, scaling limits and Loewner evolutions, 2012 (Preprint) | arXiv
[13] Conformally Invariant Processes in the Plane, Mathematical Surveys and Monographs, vol. 114, American Mathematical Society, Providence, RI, 2005
[14] Conformal invariance of planar loop-erased random walks and uniform spanning trees, Ann. Probab., Volume 32 (2004) no. 1B, pp. 939-995
[15] Boundary Behaviour of Conformal Maps, Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Sciences, vol. 299, Springer-Verlag, Berlin, 1992
[16] Scaling limits of loop-erased random walks and uniform spanning trees, Isr. J. Math., Volume 118 (2000), pp. 221-288
[17] Towards conformal invariance of 2D lattice models, International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zurich, 2006, pp. 1421-1451
[18] Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model, Ann. Math., Volume 172 (2010) no. 2, pp. 1435-1467
- Hypergeometric SLE with κ=8: Convergence of UST and LERW in topological rectangles, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 61 (2025) no. 2 | DOI:10.1214/23-aihp1446
- Delocalisation and continuity in 2D: loop
, six-vertex, and random-cluster models, Communications in Mathematical Physics, Volume 406 (2025) no. 5, p. 59 (Id/No 108) | DOI:10.1007/s00220-025-05259-9 | Zbl:8030971 - Two-Loop Loewner Potentials, International Mathematics Research Notices, Volume 2025 (2025) no. 11 | DOI:10.1093/imrn/rnaf133
- The scaling limit of boundary spin correlations in non-integrable Ising models, Journal of Mathematical Physics, Volume 66 (2025) no. 2, p. 41 (Id/No 023301) | DOI:10.1063/5.0235381 | Zbl:7993802
- The fuzzy Potts model in the plane: scaling limits and arm exponents, Probability Theory and Related Fields, Volume 191 (2025) no. 1-2, pp. 287-359 | DOI:10.1007/s00440-024-01319-8 | Zbl:7990325
- On the Role of Loewner Entropy in the Statistical Mechanics of the 2D Ising System, Progress of Theoretical and Experimental Physics, Volume 2025 (2025) no. 2 | DOI:10.1093/ptep/ptaf017
- Conformal covariance of connection probabilities in the 2D critical FK-Ising model, Stochastic Processes and their Applications, Volume 189 (2025), p. 104734 | DOI:10.1016/j.spa.2025.104734
- Macroscopic loops in the loop
model via the XOR trick, The Annals of Probability, Volume 53 (2025) no. 2, pp. 478-508 | DOI:10.1214/24-aop1712 | Zbl:8050989 - Integrability of SLE via conformal welding of random surfaces, Communications on Pure and Applied Mathematics, Volume 77 (2024) no. 5, pp. 2651-2707 | DOI:10.1002/cpa.22180 | Zbl:1543.81066
- SLE partition functions via conformal welding of random surfaces, IMRN. International Mathematics Research Notices, Volume 2024 (2024) no. 24, pp. 14763-14801 | DOI:10.1093/imrn/rnae260 | Zbl:7986123
- Multiple Ising Interfaces in Annulus and 2N-Sided Radial SLE, International Mathematics Research Notices, Volume 2024 (2024) no. 6, p. 5326 | DOI:10.1093/imrn/rnad252
- Interfaces of the two-dimensional voter model in the context of SLE, Journal of Statistical Mechanics: Theory and Experiment, Volume 2024 (2024) no. 11, p. 113203 | DOI:10.1088/1742-5468/ad8225
- Limits of conformal images and conformal images of limits for planar random curves, L'Enseignement Mathématique. 2e Série, Volume 70 (2024) no. 3-4, pp. 385-423 | DOI:10.4171/lem/1066 | Zbl:1548.60041
- Conformal invariance in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii equation, Physical Review A, Volume 109 (2024) no. 6 | DOI:10.1103/physreva.109.l061302
- Conformal Invariance in Water-Wave Turbulence, Physical Review Letters, Volume 132 (2024) no. 9 | DOI:10.1103/physrevlett.132.094001
- Connection probabilities of multiple FK-Ising interfaces, Probability Theory and Related Fields, Volume 189 (2024) no. 1-2, pp. 281-367 | DOI:10.1007/s00440-024-01269-1 | Zbl:1541.82002
- Schnyder woods,
, and Liouville quantum gravity, Transactions of the American Mathematical Society, Volume 377 (2024) no. 4, pp. 2439-2493 | DOI:10.1090/tran/8887 | Zbl:1543.60097 - Conformal field theory for annulus SLE: partition functions and martingale-observables, Analysis and Mathematical Physics, Volume 13 (2023) no. 1, p. 87 (Id/No 1) | DOI:10.1007/s13324-022-00761-y | Zbl:7624354
- Energy correlations of non-integrable Ising models: the scaling limit in the cylinder, Communications in Mathematical Physics, Volume 397 (2023) no. 1, pp. 393-483 | DOI:10.1007/s00220-022-04481-z | Zbl:7676189
- What is a random surface?, International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 2. Plenary lectures, Berlin: European Mathematical Society (EMS), 2023, pp. 1202-1258 | DOI:10.4171/icm2022/187 | Zbl:1533.60076
- Scaling limits and universality of Ising and dimer models, International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 5. Sections 9–11, Berlin: European Mathematical Society (EMS), 2023, pp. 4040-4072 | DOI:10.4171/icm2022/131 | Zbl:1535.82014
- Percolation on triangulations: a bijective path to Liouville quantum gravity, Memoirs of the American Mathematical Society, 1440, Providence, RI: American Mathematical Society (AMS), 2023 | DOI:10.1090/memo/1440 | Zbl:7753145
- Crossing probabilities of multiple Ising interfaces, The Annals of Applied Probability, Volume 33 (2023) no. 4, pp. 3169-3206 | DOI:10.1214/22-aap1888 | Zbl:1520.82015
- Universality of spin correlations in the Ising model on isoradial graphs, The Annals of Probability, Volume 51 (2023) no. 3, pp. 840-898 | DOI:10.1214/22-aop1595 | Zbl:1517.82012
- On testing for parameters in Ising models, Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, Volume 58 (2022) no. 1, pp. 164-187 | DOI:10.1214/21-aihp1157 | Zbl:1493.62039
- Convergence of fermionic observables in the massive planar FK-Ising model, Communications in Mathematical Physics, Volume 396 (2022) no. 3, pp. 1071-1133 | DOI:10.1007/s00220-022-04488-6 | Zbl:1504.82012
- Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscape, Electronic Journal of Probability, Volume 27 (2022), p. 44 (Id/No 1) | DOI:10.1214/21-ejp706 | Zbl:1496.60115
- Planar random-cluster model: scaling relations, Forum of Mathematics, Pi, Volume 10 (2022), p. 83 (Id/No e23) | DOI:10.1017/fmp.2022.16 | Zbl:1512.60065
- Slit-strip Ising boundary conformal field theory. I: Discrete and continuous function spaces, Mathematical Physics, Analysis and Geometry, Volume 25 (2022) no. 4, p. 53 (Id/No 30) | DOI:10.1007/s11040-022-09442-5 | Zbl:1508.30085
- Permutation-Loewner entropy analysis for 2-dimensional Ising system interface, Physica A: Statistical Mechanics and its Applications, Volume 594 (2022), p. 126943 | DOI:10.1016/j.physa.2022.126943
- A formula for boundary correlations of the critical Ising model, Probability Theory and Related Fields, Volume 182 (2022) no. 1-2, pp. 615-640 | DOI:10.1007/s00440-021-01086-w | Zbl:1482.82021
- The two-dimensional continuum random field Ising model, The Annals of Probability, Volume 50 (2022) no. 2, pp. 419-454 | DOI:10.1214/21-aop1536 | Zbl:1489.82040
- On multiple SLE for the FK-Ising model, The Annals of Probability, Volume 50 (2022) no. 2, pp. 771-790 | DOI:10.1214/21-aop1547 | Zbl:1486.60106
- Uniform Lipschitz functions on the triangular lattice have logarithmic variations, Communications in Mathematical Physics, Volume 381 (2021) no. 3, pp. 1153-1221 | DOI:10.1007/s00220-020-03920-z | Zbl:1470.60278
- Rate of convergence of critical interfaces to SLE curves, Extended abstracts fall 2019. Spaces of analytic functions: approximation, interpolation, sampling, SAFAIS 2019 program, Centre de Recerca Matemàtica, Barcelona, Spain, October–December 2019, Cham: Birkhäuser, 2021, pp. 43-50 | DOI:10.1007/978-3-030-74417-5_7 | Zbl:1504.30001
- Three phases of multiple SLE driven by non-colliding Dyson's Brownian motions, Journal of Physics A: Mathematical and Theoretical, Volume 54 (2021) no. 32, p. 19 (Id/No 325002) | DOI:10.1088/1751-8121/ac0dee | Zbl:1519.60093
- Macroscopic loops in the loop
model at Nienhuis' critical point, Journal of the European Mathematical Society (JEMS), Volume 23 (2021) no. 1, pp. 315-347 | DOI:10.4171/jems/1012 | Zbl:1477.60137 - Planar random-cluster model: fractal properties of the critical phase, Probability Theory and Related Fields, Volume 181 (2021) no. 1-3, pp. 401-449 | DOI:10.1007/s00440-021-01060-6 | Zbl:1475.60195
- Permutation-Loewner Entropy Analysis for 2-Dimensional Ising System Interface, SSRN Electronic Journal (2021) | DOI:10.2139/ssrn.3989699
- On the uniqueness of global multiple SLEs, The Annals of Probability, Volume 49 (2021) no. 1, pp. 400-434 | DOI:10.1214/20-aop1477 | Zbl:1478.60225
- Loewner driving force of the interface in the 2-dimensional Ising system as a chaotic dynamical system, Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 30 (2020) no. 11 | DOI:10.1063/5.0023261
- The expectation value of the number of loops and the left-passage probability in the double-dimer model, Communications in Mathematical Physics, Volume 373 (2020) no. 1, pp. 357-388 | DOI:10.1007/s00220-019-03620-3 | Zbl:1475.82004
- Hypergeometric SLE: conformal Markov characterization and applications, Communications in Mathematical Physics, Volume 374 (2020) no. 2, pp. 433-484 | DOI:10.1007/s00220-020-03697-1 | Zbl:1473.82021
- Critical Ising model on random triangulations of the disk: enumeration and local limits, Communications in Mathematical Physics, Volume 374 (2020) no. 3, pp. 1577-1643 | DOI:10.1007/s00220-019-03672-5 | Zbl:1437.82004
- Ising model and the positive orthogonal Grassmannian, Duke Mathematical Journal, Volume 169 (2020) no. 10, pp. 1877-1942 | DOI:10.1215/00127094-2019-0086 | Zbl:1446.82008
- A support theorem for SLE curves, Electronic Journal of Probability, Volume 25 (2020), p. 18 (Id/No 18) | DOI:10.1214/20-ejp425 | Zbl:1439.30021
- UST branches, martingales, and multiple SLE(2), Electronic Journal of Probability, Volume 25 (2020), p. 37 (Id/No 83) | DOI:10.1214/20-ejp485 | Zbl:1459.60175
- Conformal welding problem, flow line problem, and multiple Schramm-Loewner evolution, Journal of Mathematical Physics, Volume 61 (2020) no. 8, p. 083301 | DOI:10.1063/1.5145357 | Zbl:1454.81194
- On the convergence of FK-Ising percolation to
, Journal of Theoretical Probability, Volume 33 (2020) no. 2, pp. 828-865 | DOI:10.1007/s10959-019-00950-9 | Zbl:1434.60230 - Particles, string and interface in the three-dimensional Ising model, Nuclear Physics. B, Volume 958 (2020), p. 11 (Id/No 115139) | DOI:10.1016/j.nuclphysb.2020.115139 | Zbl:1479.82010
- Lectures on the Ising and Potts models on the hypercubic lattice, Random graphs, phase transitions, and the Gaussian free field. Lecture notes given at the PIMS-CRM summer school in probability, University of British Columbia, Vancouver, Canada, June 5–30, 2017, Cham: Springer, 2020, pp. 35-161 | DOI:10.1007/978-3-030-32011-9_2 | Zbl:1447.82007
- Global and local multiple SLEs for
and connection probabilities for level lines of GFF, Communications in Mathematical Physics, Volume 366 (2019) no. 2, pp. 469-536 | DOI:10.1007/s00220-019-03360-4 | Zbl:1422.60142 - Ising model: local spin correlations and conformal invariance, Communications in Mathematical Physics, Volume 367 (2019) no. 3, pp. 771-833 | DOI:10.1007/s00220-019-03312-y | Zbl:1419.82012
- Conformal invariance of boundary touching loops of FK Ising model, Communications in Mathematical Physics, Volume 369 (2019) no. 1, pp. 49-98 | DOI:10.1007/s00220-019-03437-0 | Zbl:1422.60140
- Spin Systems, Introduction to a Renormalisation Group Method, Volume 2242 (2019), p. 3 | DOI:10.1007/978-981-32-9593-3_1
- Emergent planarity in two-dimensional Ising models with finite-range interactions, Inventiones Mathematicae, Volume 216 (2019) no. 3, pp. 661-743 | DOI:10.1007/s00222-018-00851-4 | Zbl:1417.82022
- Sharp threshold phenomena in statistical physics, Japanese Journal of Mathematics. 3rd Series, Volume 14 (2019) no. 1, pp. 1-25 | DOI:10.1007/s11537-018-1726-x | Zbl:1420.82003
- Toward a conformal field theory for Schramm-Loewner evolutions, Journal of Mathematical Physics, Volume 60 (2019) no. 10, p. 103305 | DOI:10.1063/1.5094364 | Zbl:1431.82020
- Schramm-Loewner-evolution-type growth processes corresponding to Wess-Zumino-Witten theories, Letters in Mathematical Physics, Volume 109 (2019) no. 6, pp. 1397-1413 | DOI:10.1007/s11005-018-01150-y | Zbl:1469.60258
- Conformal invariance in the FK-representation of the quantum Ising model and convergence of the interface to the
, Probability Theory and Related Fields, Volume 173 (2019) no. 1-2, pp. 87-156 | DOI:10.1007/s00440-018-0831-3 | Zbl:1417.82012 - Self-avoiding walk, spin systems and renormalization, Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences, Volume 475 (2019) no. 2221, p. 21 (Id/No 20180549) | DOI:10.1098/rspa.2018.0549 | Zbl:1425.82008
- Numerical study on a crossing probability for the four-state Potts model: Logarithmic correction to the finite-size scaling, Progress of Theoretical and Experimental Physics, Volume 2019 (2019) no. 9 | DOI:10.1093/ptep/ptz101
- Coset construction of Virasoro minimal models and coupling of Wess-Zumino-Witten theory with Schramm-Loewner evolution, Reviews in Mathematical Physics, Volume 31 (2019) no. 10, p. 16 (Id/No 1950037) | DOI:10.1142/s0129055x19500375 | Zbl:1432.60078
- Lectures on the Spin and Loop O(n) Models, Sojourns in Probability Theory and Statistical Physics - I, Volume 298 (2019), p. 246 | DOI:10.1007/978-981-15-0294-1_10
- Bipolar orientations on planar maps and
, The Annals of Probability, Volume 47 (2019) no. 3, pp. 1240-1269 | DOI:10.1214/18-aop1282 | Zbl:1466.60170 - The scaling limit of critical Ising interfaces is
, The Annals of Probability, Volume 47 (2019) no. 4, pp. 2049-2086 | DOI:10.1214/18-aop1301 | Zbl:1467.60061 - Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines, Communications in Mathematical Physics, Volume 361 (2018) no. 1, pp. 53-80 | DOI:10.1007/s00220-018-3159-z | Zbl:1430.60064
- Connection probabilities for conformal loop ensembles, Communications in Mathematical Physics, Volume 362 (2018) no. 2, pp. 415-453 | DOI:10.1007/s00220-018-3207-8 | Zbl:1400.60128
- SLE as a mating of trees in Euclidean geometry, Communications in Mathematical Physics, Volume 364 (2018) no. 1, pp. 171-201 | DOI:10.1007/s00220-018-3149-1 | Zbl:1408.60073
- Universality for the random-cluster model on isoradial graphs, Electronic Journal of Probability, Volume 23 (2018), p. 70 (Id/No 96) | DOI:10.1214/18-ejp223 | Zbl:1414.60076
- 2D Ising model: correlation functions at criticality via Riemann-type boundary value problems, European congress of mathematics. Proceedings of the 7th ECM (7ECM) congress, Berlin, Germany, July 18–22, 2016, Zürich: European Mathematical Society (EMS), 2018, pp. 235-256 | DOI:10.4171/176-1/10 | Zbl:1402.82005
- Random currents expansion of the Ising model, European congress of mathematics. Proceedings of the 7th ECM (7ECM) congress, Berlin, Germany, July 18–22, 2016, Zürich: European Mathematical Society (EMS), 2018, pp. 869-889 | DOI:10.4171/176-1/39 | Zbl:1403.82005
- Schramm-Loewner evolution with Lie superalgebra symmetry, International Journal of Modern Physics A, Volume 33 (2018) no. 20, p. 17 (Id/No 1850117) | DOI:10.1142/s0217751x18501178 | Zbl:1393.60091
- Local martingales associated with Schramm-Loewner evolutions with internal symmetry, Journal of Mathematical Physics, Volume 59 (2018) no. 10, p. 101703 | DOI:10.1063/1.5034416 | Zbl:1402.60103
- Schramm's formula for multiple loop-erased random walks, Journal of Statistical Mechanics: Theory and Experiment, Volume 2018 (2018) no. 10, p. 66 (Id/No 103106) | DOI:10.1088/1742-5468/aae5a6 | Zbl:1457.82158
- Polychromatic arm exponents for the critical planar FK-Ising model, Journal of Statistical Physics, Volume 170 (2018) no. 6, pp. 1177-1196 | DOI:10.1007/s10955-018-1983-3 | Zbl:1392.82012
- Alternating arm exponents for the critical planar Ising model, The Annals of Probability, Volume 46 (2018) no. 5, pp. 2863-2907 | DOI:10.1214/17-aop1241 | Zbl:1428.60119
- Simple CLE in doubly connected domains, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 53 (2017) no. 2 | DOI:10.1214/15-aihp726
- Continuity of the phase transition for planar random-cluster and Potts models with
, Communications in Mathematical Physics, Volume 349 (2017) no. 1, pp. 47-107 | DOI:10.1007/s00220-016-2759-8 | Zbl:1357.82011 - Exponential decay of loop lengths in the loop
model with large , Communications in Mathematical Physics, Volume 349 (2017) no. 3, pp. 777-817 | DOI:10.1007/s00220-016-2815-4 | Zbl:1359.82007 - Convergence of the two-dimensional dynamic Ising-Kac model to
, Communications on Pure and Applied Mathematics, Volume 70 (2017) no. 4, pp. 717-812 | DOI:10.1002/cpa.21655 | Zbl:1364.82013 - Boundary arm exponents for SLE, Electronic Journal of Probability, Volume 22 (2017) no. none | DOI:10.1214/17-ejp110
- CLE percolations, Forum of Mathematics, Pi, Volume 5 (2017), p. 102 (Id/No e4) | DOI:10.1017/fmp.2017.5 | Zbl:1390.60356
- Fermionic observables in the transverse Ising chain, Journal of Mathematical Physics, Volume 58 (2017) no. 5, p. 053302 | DOI:10.1063/1.4982637 | Zbl:1368.82002
- Six-vertex model and Schramm-Loewner evolution, Physical Review E, Volume 95 (2017) no. 5 | DOI:10.1103/physreve.95.052146
- Critical Ising interfaces in multiply-connected domains, Probability Theory and Related Fields, Volume 167 (2017) no. 1-2, pp. 379-415 | DOI:10.1007/s00440-015-0685-x | Zbl:1364.82012
- Intersections of SLE paths: the double and cut point dimension of SLE, Probability Theory and Related Fields, Volume 167 (2017) no. 1-2, pp. 45-105 | DOI:10.1007/s00440-015-0677-x | Zbl:1408.60074
- Level lines of Gaussian free field. I: Zero-boundary GFF., Stochastic Processes and their Applications, Volume 127 (2017) no. 4, pp. 1045-1124 | DOI:10.1016/j.spa.2016.07.009 | Zbl:1358.60066
- Random curves, scaling limits and Loewner evolutions, The Annals of Probability, Volume 45 (2017) no. 2 | DOI:10.1214/15-aop1074
- SLE boundary visits, Annales Henri Poincaré, Volume 17 (2016) no. 6, pp. 1263-1330 | DOI:10.1007/s00023-015-0452-7 | Zbl:1346.82012
- Planar Ising magnetization field II. Properties of the critical and near-critical scaling limits, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 52 (2016) no. 1 | DOI:10.1214/14-aihp643
- Conformal invariance of crossing probabilities for the Ising model with free boundary conditions, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 52 (2016) no. 4 | DOI:10.1214/15-aihp698
- Pure partition functions of multiple SLEs, Communications in Mathematical Physics, Volume 346 (2016) no. 1, pp. 237-292 | DOI:10.1007/s00220-016-2655-2 | Zbl:1358.82012
- Conformal correlation functions in the Brownian loop soup, Nuclear Physics. B, Volume 902 (2016), pp. 483-507 | DOI:10.1016/j.nuclphysb.2015.11.022 | Zbl:1332.82083
- Active spanning trees and Schramm-Loewner evolution, Physical Review E, Volume 93 (2016) no. 6 | DOI:10.1103/physreve.93.062121
- The phase transitions of the planar random-cluster and Potts models with
are sharp, Probability Theory and Related Fields, Volume 164 (2016) no. 3-4, pp. 865-892 | DOI:10.1007/s00440-015-0621-0 | Zbl:1356.60167 - The nested simple conformal loop ensembles in the Riemann sphere, Probability Theory and Related Fields, Volume 165 (2016) no. 3-4, pp. 835-866 | DOI:10.1007/s00440-015-0647-3 | Zbl:1352.60117
- Random walk loop soups and conformal loop ensembles, Probability Theory and Related Fields, Volume 166 (2016) no. 1-2, pp. 553-584 | DOI:10.1007/s00440-015-0666-0 | Zbl:1357.60049
- Critical point and duality in planar lattice models, Probability and statistical physics in St. Petersburg. St. Petersburg School Probability and Statistical Physics, St. Petersburg State University, St. Petersburg, Russia, June 18–29, 2012, Providence, RI: American Mathematical Society (AMS), 2016, pp. 51-98 | Zbl:1391.82006
- Robust discrete complex analysis: a toolbox, The Annals of Probability, Volume 44 (2016) no. 1, pp. 628-683 | DOI:10.1214/14-aop985 | Zbl:1347.60050
- Conformal invariance of spin correlations in the planar Ising model, Annals of Mathematics. Second Series, Volume 181 (2015) no. 3, pp. 1087-1138 | DOI:10.4007/annals.2015.181.3.5 | Zbl:1318.82006
- Smirnov's observable for free boundary conditions, interfaces and crossing probabilities, Communications in Mathematical Physics, Volume 337 (2015) no. 1, pp. 225-252 | DOI:10.1007/s00220-015-2339-3 | Zbl:1318.82010
- Height fluctuations in non-integrable classical dimers, EPL (Europhysics Letters), Volume 109 (2015) no. 6, p. 60004 | DOI:10.1209/0295-5075/109/60004
- On the critical parameters of the
random-cluster model on isoradial graphs, Journal of Physics A: Mathematical and Theoretical, Volume 48 (2015) no. 48, p. 28 (Id/No 484003) | DOI:10.1088/1751-8113/48/48/484003 | Zbl:1342.82018 - The voter model chordal interface in two dimensions, Journal of Statistical Physics, Volume 159 (2015) no. 4, pp. 937-957 | DOI:10.1007/s10955-015-1198-9 | Zbl:1328.82024
- Recent advances in percolation theory and its applications, Physics Reports, Volume 578 (2015), pp. 1-32 | DOI:10.1016/j.physrep.2015.03.003 | Zbl:1357.82032
- Planar Ising magnetization field. I: Uniqueness of the critical scaling limit, The Annals of Probability, Volume 43 (2015) no. 2, pp. 528-571 | DOI:10.1214/13-aop881 | Zbl:1332.82012
- The near-critical planar FK-Ising model, Communications in Mathematical Physics, Volume 326 (2014) no. 1, pp. 1-35 | DOI:10.1007/s00220-013-1857-0 | Zbl:1286.82003
- The Hausdorff dimension of the CLE gasket, The Annals of Probability, Volume 42 (2014) no. 4, pp. 1644-1665 | DOI:10.1214/12-aop820 | Zbl:1305.60078
- Ising interfaces and free boundary conditions, Journal of the American Mathematical Society, Volume 26 (2013) no. 4, pp. 1107-1189 | DOI:10.1090/s0894-0347-2013-00774-2 | Zbl:1284.82021
- Universality in the 2D Ising model and conformal invariance of fermionic observables, Inventiones Mathematicae, Volume 189 (2012) no. 3, pp. 515-580 | DOI:10.1007/s00222-011-0371-2 | Zbl:1257.82020
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