[Pantalon de Feller]
Nous definissons un espace de Banach E associé a l'espace des lacets tel qu'un pantalon aléatoire réalise une application continue de dans E. Nous sommes motivés par l'un des axiomes de G. Segal de la théorie des champs conformes. Les détails seront écrits dans un prochain article.
Given a manifold M we define a Banach space E associated with the loop space of M in such a way that the random pants realize a continuous map from the injective tensor product into E. Our research is motivated by one of the axioms of conformal field theory of G. Segal. Full details will be presented in a forthcoming article.
Accepté le :
Publié le :
@article{CRMATH_2006__343_5_333_0,
author = {Zdzis{\l}aw Brze\'zniak and Remi L\'eandre},
title = {Fellerian pants},
journal = {Comptes Rendus. Math\'ematique},
pages = {333--338},
publisher = {Elsevier},
volume = {343},
number = {5},
year = {2006},
doi = {10.1016/j.crma.2006.07.003},
language = {en},
}
Zdzisław Brzeźniak; Remi Léandre. Fellerian pants. Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 333-338. doi : 10.1016/j.crma.2006.07.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.07.003/
[1] H. Airault, P. Malliavin, Quasi-sure analysis, Publication of University Paris VI, 1990
[2] H. Airault, P. Malliavin, Analysis over loop groups, Publication of University Paris VI, 1991
[3] Stochastic Equations and Differential Geometry, Mathematics and Its Applications, vol. 30, Kluwer Academic Publishers, Dordrecht, 1990
[4] Large deviations and the Malliavin Calculus, Progress in Mathematics, vol. 45, Birkhäuser, Boston, 1984
[5] Stochastic differential equations on Banach manifolds; applications to diffusions on loop spaces, MFAT, Volume 6 (2000) no. 1, pp. 43-84 (a special volume dedicated to the memory of Professor Yuri Daletski)
[6] Horizontal lift of an infinite dimensional diffusion, Potential Anal., Volume 12 (2000), pp. 249-280
[7] Z. Brzeźniak, R. Léandre, Stochastic pants over a Riemannian manifold, in preparation
[8] Conditioning a lifted stochastic system in a product space, Ann. Probab., Volume 16 (1988) no. 4, pp. 1840-1853
[9] Stochastic Differential Equations on Manifolds, London Math. Soc. Lecture Notes Ser., vol. 70, Cambridge University Press, 1982
[10] Spectra of Wess–Zumino–Witten models with arbitrary simple groups, Comm. Math. Phys., Volume 117 (1988) no. 1, pp. 127-158
[11] K. Gawȩdzki, Conformal field theory, Séminaire Bourbaki, Vol. 1988/89; Astérisque No. 177–178, Exp. No. 704 (1989) 95–126
[12] Quasi sure stochastic flows, Stochastics Stochastics Rep., Volume 33 (1990) no. 3–4, pp. 149-157
[13] Diffusion and Brownian Motion on infinite dimensional manifolds, Trans. Amer. Math. Soc., Volume 169 (1972), pp. 439-459
[14] Analysis over loop space and topology, Math. Notes, Volume 72 (2002), pp. 212-229
[15] Brownian surfaces with boundary and Deligne cohomology, Rep. Math. Phys., Volume 52 (2003), pp. 353-362
[16] Markov property and operads, Entropy, Volume 6 (2004), pp. 180-215
[17] Two examples of stochastic field theories, Osaka J. Math., Volume 42 (2005), pp. 353-365
[18] Brownian pants and Deligne cohomology, J. Math. Phys., Volume 46 (2005) no. 1–20, p. 033503
[19] R. Léandre, Galton–Watson tree and branching loops, in: I. Mladenov, A. Hirschfeld (Eds.), Geometry, Integrability and Quantization, Softek, 2005, pp. 267–283
[20] Stochastic Analysis, Springer, Berlin, 1997
[21] Flot d'une équation différentielle stochastique (J. Azéma; M. Yor, eds.), Séminaire de Probabilités XV, Lecture Notes in Math., vol. 850, Springer, Berlin, 1981, pp. 100-117
[22] Diffusion processes and Riemannian geometry, Russian Math. Surveys, Volume 30 (1975), pp. 1-63
[23] Two-dimensional conformal field theories and modular functors, IXth International Congress on Mathematical Physics (Swansea, 1988), Hilger, Bristol, 1989, pp. 22-37
[24] Positive generalized Wiener functions and potential theory over abstract Wiener spaces, Osaka. J. Math., Volume 25 (1988), pp. 665-696
Cité par Sources :
Commentaires - Politique