Comptes Rendus
Probability Theory
On the diffusive behavior of isotropic diffusions in a random environment
Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 429-434.

We present here results concerning the asymptotic behavior of isotropic diffusions in random environment that are small perturbations of Brownian motion. When the space dimension is three or more we prove an invariance principle as well as transience. Our methods also apply to questions of homogenization in random media.

Nous présentons ici des résultats sur le comportement asymptotique de diffusions isotropes en milieu aléatoire, qui sont de petites perturbations du mouvement brownien. Lorsque la dimension de l'espace est trois ou plus nous prouvons un principe d'invariance et la transience de la diffusion. Nos méthodes s'appliquent aussi à des problèmes d'homogénéisation en milieu aléatoire.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.07.012
Alain-Sol Sznitman 1; Ofer Zeitouni 2, 3

1 Departement Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
2 Department of Mathematics, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN 55455, USA
3 Departments of Electrical Engineering and of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel
@article{CRMATH_2004__339_6_429_0,
     author = {Alain-Sol Sznitman and Ofer Zeitouni},
     title = {On the diffusive behavior of isotropic diffusions in a random environment},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {429--434},
     publisher = {Elsevier},
     volume = {339},
     number = {6},
     year = {2004},
     doi = {10.1016/j.crma.2004.07.012},
     language = {en},
}
TY  - JOUR
AU  - Alain-Sol Sznitman
AU  - Ofer Zeitouni
TI  - On the diffusive behavior of isotropic diffusions in a random environment
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 429
EP  - 434
VL  - 339
IS  - 6
PB  - Elsevier
DO  - 10.1016/j.crma.2004.07.012
LA  - en
ID  - CRMATH_2004__339_6_429_0
ER  - 
%0 Journal Article
%A Alain-Sol Sznitman
%A Ofer Zeitouni
%T On the diffusive behavior of isotropic diffusions in a random environment
%J Comptes Rendus. Mathématique
%D 2004
%P 429-434
%V 339
%N 6
%I Elsevier
%R 10.1016/j.crma.2004.07.012
%G en
%F CRMATH_2004__339_6_429_0
Alain-Sol Sznitman; Ofer Zeitouni. On the diffusive behavior of isotropic diffusions in a random environment. Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 429-434. doi : 10.1016/j.crma.2004.07.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.012/

[1] E. Bolthausen; A.S. Sznitman Ten Lectures on Random Media, DMV Seminar, vol. 32, Birkhäuser, Basel, 2002

[2] J. Bricmont; A. Kupiainen Random walks in asymmetric random environments, Commun. Math. Phys., Volume 142 (1991) no. 2, pp. 345-420

[3] A. De Masi; P.A. Ferrari; S. Goldstein; W.D. Wick An invariance principle for reversible Markov processes, applications to random motions in random environments, J. Statist. Phys., Volume 55 (1989) no. 3–4, pp. 787-855

[4] R.M. Dudley Real Analysis and Probability, Wadsworth, Belmont, CA, 1989

[5] C. Kipnis; S.R.S. Varadhan A central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Commun. Math. Phys., Volume 104 (1986), pp. 1-19

[6] S.M. Kozlov The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys, Volume 40 (1985) no. 2, pp. 73-145

[7] S.A. Molchanov Lectures on random media, Lecture Notes in Math., vol. 1581, Springer, Berlin, 1994, pp. 242-411

[8] S. Olla Central limit theorems for tagged particles and for diffusions in random environment, Milieux Aléatoires, Panoramas et Synthèses, vol. 12, Société Mathématique de France, 2001

[9] G. Papanicolaou; S.R.S. Varadhan Boundary value problems with rapidly oscillating random coefficients (J. Fritz; D. Szasz, eds.), Random Fields, Janyos Bolyai Series, North-Holland, Amsterdam, 1981, pp. 835-873

[10] A.S. Sznitman Topics in random walk in random environment, Notes of course at School and Conference on Probability Theory, May 2002, Trieste, ICTP Lecture Series, 2004, pp. 203-266

[11] A.S. Sznitman, O. Zeitouni, An invariance principle for isotropic diffusions in random environment, Preprint

[12] V.V. Yurinsky Average of an elliptic boundary problem with random coefficients, Siberian Math. J., Volume 21 (1980), pp. 470-482

[13] O. Zeitouni Random walks in random environment (J. Picard, ed.), Lectures on Probability Theory and Statistics, Lecture Notes in Math, vol. 1837, Springer, Berlin, 2004, pp. 190-312

Cited by Sources:

Comments - Policy


Articles of potential interest

Large deviation principle for a backward stochastic differential equation with subdifferential operator

El Hassan Essaky

C. R. Math (2008)