Fellerian pants

Zdzisław Brzeźniak; Remi Léandre

doi:10.1016/j.crma.2006.07.003

Probability Theory

Fellerian pants
[Pantalon de Feller]

Présenté par : Marc Yor

Zdzisław Brzeźniak ¹ ; Remi Léandre ²

¹ Department of Mathematics, The University of York, Heslington, York YO10 5DD, UK
² Département de mathématiques, Université de Bourgogne, 21000 Dijon, France

Comptes Rendus. Mathématique, Volume 343 (2006) no. 5, pp. 333-338.

Résumé
Abstract

Nous definissons un espace de Banach E associé a l'espace des lacets tel qu'un pantalon aléatoire réalise une application continue de $E {\hat{\otimes}}_{ε} E$ 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 $L (M)$ of M in such a way that the random pants realize a continuous map from the injective tensor product $E {\hat{\otimes}}_{ε} E$ 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.

Reçu le : 2004-02-15
Accepté le : 2006-06-23
Publié le : 2006-08-14

DOI : 10.1016/j.crma.2006.07.003

Affiliations des auteurs :

Zdzisław Brzeźniak ¹ ; Remi Léandre ²

¹ Department of Mathematics, The University of York, Heslington, York YO10 5DD, UK
² Département de mathématiques, Université de Bourgogne, 21000 Dijon, France

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     title = {Fellerian pants},
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     pages = {333--338},
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     number = {5},
     year = {2006},
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     language = {en},
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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/

Bibliographie
Cité par

[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] Ya.L. Belopolskaya; Yu.L. Daletski Stochastic Equations and Differential Geometry, Mathematics and Its Applications, vol. 30, Kluwer Academic Publishers, Dordrecht, 1990

[4] J.-M. Bismut Large deviations and the Malliavin Calculus, Progress in Mathematics, vol. 45, Birkhäuser, Boston, 1984

[5] Z. Brzeźniak; K.D. Elworthy 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] Z. Brzeźniak; R. Léandre 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] A. Carverhill Conditioning a lifted stochastic system in a product space, Ann. Probab., Volume 16 (1988) no. 4, pp. 1840-1853

[9] K.D. Elworthy Stochastic Differential Equations on Manifolds, London Math. Soc. Lecture Notes Ser., vol. 70, Cambridge University Press, 1982

[10] G. Felder; K. Gawȩdzki; A. Kupiainen 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] Z.Y. Huang; J.G. Ren Quasi sure stochastic flows, Stochastics Stochastics Rep., Volume 33 (1990) no. 3–4, pp. 149-157

[13] H.H. Kuo Diffusion and Brownian Motion on infinite dimensional manifolds, Trans. Amer. Math. Soc., Volume 169 (1972), pp. 439-459

[14] R. Léandre Analysis over loop space and topology, Math. Notes, Volume 72 (2002), pp. 212-229

[15] R. Léandre Brownian surfaces with boundary and Deligne cohomology, Rep. Math. Phys., Volume 52 (2003), pp. 353-362

[16] R. Léandre Markov property and operads, Entropy, Volume 6 (2004), pp. 180-215

[17] R. Léandre Two examples of stochastic field theories, Osaka J. Math., Volume 42 (2005), pp. 353-365

[18] R. Léandre 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] P. Malliavin Stochastic Analysis, Springer, Berlin, 1997

[21] P.A. Meyer 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] S. Molchanov Diffusion processes and Riemannian geometry, Russian Math. Surveys, Volume 30 (1975), pp. 1-63

[23] G. Segal Two-dimensional conformal field theories and modular functors, IXth International Congress on Mathematical Physics (Swansea, 1988), Hilger, Bristol, 1989, pp. 22-37

[24] H. Sugita Positive generalized Wiener functions and potential theory over abstract Wiener spaces, Osaka. J. Math., Volume 25 (1988), pp. 665-696

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