Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions

Alexander I. Bufetov; Yanqi Qiu

doi:10.1016/j.crma.2015.03.018

Dynamical systems/Probability theory

Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions
[Équivalence de measures de Palm pour les processus déterminantaux associés aux espaces de Hilbert des fonctions holomorphes]

Présenté par : Michel Talagrand

Alexander I. Bufetov ^1,^2,^3,^4,⁵ ; Yanqi Qiu ¹

¹ Aix-Marseille Université, Centrale Marseille, CNRS, I2M, UMR7373, 39, rue Frédéric-Juliot-Curie, 13453 Marseille, France
² Steklov Institute of Mathematics, Moscow, Russian Federation
³ Institute for Information Transmission Problems, Moscow, Russian Federation
⁴ National Research University Higher School of Economics, Moscow, Russian Federation
⁵ Rice University, Houston, TX, United States

Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 551-555.

Résumé
Abstract

On obtient des formules explicites, sous forme des fonctionnelles multiplicatives régularisées liées à certains produits de Blaschke, des dérivées de Radon–Nikodym entre toutes les mesures de Palm pour les processus déterminantaux associés aux espaces de Bergman pondérés sur le disque. Notre méthode s'applique également aux processus déterminantaux associés aux espaces de Fock pondérés.

We obtain explicit formulae, in the form of regularized multiplicative functionals related to certain Blaschke products, of the Radon–Nikodym derivatives between reduced Palm measures of all orders for determinantal point processes associated with a large class of weighted Bergman spaces on the disk. Our method also applies to determinantal point processes associated with weighted Fock spaces.

Reçu le : 2015-01-29
Accepté le : 2015-03-04
Publié le : 2015-04-27

DOI : 10.1016/j.crma.2015.03.018

Affiliations des auteurs :

Alexander I. Bufetov ^{1, 2, 3, 4, 5} ; Yanqi Qiu ¹

¹ Aix-Marseille Université, Centrale Marseille, CNRS, I2M, UMR7373, 39, rue Frédéric-Juliot-Curie, 13453 Marseille, France
² Steklov Institute of Mathematics, Moscow, Russian Federation
³ Institute for Information Transmission Problems, Moscow, Russian Federation
⁴ National Research University Higher School of Economics, Moscow, Russian Federation
⁵ Rice University, Houston, TX, United States

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     author = {Alexander I. Bufetov and Yanqi Qiu},
     title = {Equivalence of {Palm} measures for determinantal point processes associated with {Hilbert} spaces of holomorphic functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {551--555},
     publisher = {Elsevier},
     volume = {353},
     number = {6},
     year = {2015},
     doi = {10.1016/j.crma.2015.03.018},
     language = {en},
}

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Alexander I. Bufetov; Yanqi Qiu. Equivalence of Palm measures for determinantal point processes associated with Hilbert spaces of holomorphic functions. Comptes Rendus. Mathématique, Volume 353 (2015) no. 6, pp. 551-555. doi : 10.1016/j.crma.2015.03.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.03.018/

Bibliographie
Cité par

[1] A.I. Bufetov Quasi-symmetries of determinantal point processes, Sep 2014 | arXiv

[2] S. Ghosh; Y. Peres Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues | arXiv

[3] A.E. Holroyd; T. Soo Insertion and deletion tolerance of point processes, Electron. J. Probab., Volume 18 (2013) no. 74, pp. 1-24

[4] J.B. Hough; M. Krishnapur; Y. Peres; B. Virág Determinantal processes and independence, Probab. Surv., Volume 3 (2006), pp. 206-229

[5] R. Lyons Determinantal probability measures, Publ. Math. Inst. Hautes Études Sci., Volume 98 (2003), pp. 167-212

[6] O. Macchi The coincidence approach to stochastic point processes, Adv. Appl. Probab., Volume 7 (1975), pp. 83-122

[7] G. Olshanski The quasi-invariance property for the Gamma kernel determinantal measure, Adv. Math., Volume 226 (2011) no. 3, pp. 2305-2350

[8] H. Osada; T. Shirai Absolute continuity and singularity of Palm measures of the Ginibre point process, June 2014 | arXiv

[9] Y. Peres; B. Virág Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process, Acta Math., Volume 194 (2005) no. 1, pp. 1-35

[10] T. Shirai; Y. Takahashi Random point fields associated with certain Fredholm determinants. I. Fermion, Poisson and boson point processes, J. Funct. Anal., Volume 205 (2003) no. 2, pp. 414-463

[11] T. Shirai; Y. Takahashi Random point fields associated with certain Fredholm determinants. II. Fermion shifts and their ergodic and Gibbs properties, Ann. Probab., Volume 31 (2003) no. 3, pp. 1533-1564

[12] A. Soshnikov Determinantal random point fields, Usp. Mat. Nauk, Volume 55 (2000) no. 5(335), pp. 107-160

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