Volume 24, 2020
|Page(s)||374 - 398|
|Published online||25 September 2020|
Large deviations for Brownian motion in a random potential
Univ Brest, Université de Brest, LMBA UMR CNRS 6205, 6 avenue Le Gorgeu,
Brest cedex, France.
* Corresponding author: email@example.com
Accepted: 4 February 2020
A quenched large deviation principle for Brownian motion in a stationary potential is proved. As the proofs are based on a method developed by Sznitman [Comm. Pure Appl. Math. 47 (1994) 1655–1688] for Brownian motion among obstacles with compact support no regularity conditions on the potential is needed. In particular, the sufficient conditions are verified by potentials with polynomially decaying correlations such as the classical potentials studied by Pastur [Teoret. Mat. Fiz. 32 (1977) 88–95] and Fukushima [J. Stat. Phys. 133 (2008) 639–657] and the potentials recently introduced by Lacoin [Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012) 1010–1028; 1029–1048].
Mathematics Subject Classification: 82B41 / 60K37
Key words: Brownian motion / long-range random potential / Lyapunov exponents / shape theorem / large deviations
© The authors. Published by EDP Sciences, SMAI 2020
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