Fellerian pants

Brzeźniak, Zdzisław; Léandre, Remi

doi:10.1016/j.crma.2006.07.003

Probability Theory

Fellerian pants
[Pantalon de Feller]

Présenté par : Marc Yor

Brzeźniak, Zdzisław ¹ ; Léandre, Remi 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, Tome 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 :

Brzeźniak, Zdzisław ¹ ; Léandre, Remi ²

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

@article{CRMATH_2006__343_5_333_0,
     author = {Brze\'zniak, Zdzis{\l}aw and L\'eandre, Remi},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2006.07.003/}
}

TY  - JOUR
AU  - Brzeźniak, Zdzisław
AU  - Léandre, Remi
TI  - Fellerian pants
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 333
EP  - 338
VL  - 343
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2006.07.003/
DO  - 10.1016/j.crma.2006.07.003
LA  - en
ID  - CRMATH_2006__343_5_333_0
ER  -

%0 Journal Article
%A Brzeźniak, Zdzisław
%A Léandre, Remi
%T Fellerian pants
%J Comptes Rendus. Mathématique
%D 2006
%P 333-338
%V 343
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2006.07.003/
%R 10.1016/j.crma.2006.07.003
%G en
%F CRMATH_2006__343_5_333_0

Brzeźniak, Zdzisław; Léandre, Remi. Fellerian pants. Comptes Rendus. Mathématique, Tome 343 (2006) no. 5, pp. 333-338. doi : 10.1016/j.crma.2006.07.003. http://www.numdam.org/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] Belopolskaya, Ya.L.; Daletski, Yu.L. Stochastic Equations and Differential Geometry, Mathematics and Its Applications, vol. 30, Kluwer Academic Publishers, Dordrecht, 1990

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

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

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

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

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

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

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

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

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

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

[21] Meyer, P.A. Flot d'une équation différentielle stochastique (Azéma, J.; Yor, M., eds.), Séminaire de Probabilités XV, Lecture Notes in Math., vol. 850, Springer, Berlin, 1981, pp. 100-117

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

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

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

Cité par Sources :