Large deviations for Brownian motion in a random potential
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 374-398.

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].

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DOI : 10.1051/ps/2020007
Classification : 82B41, 60K37
Mots-clés : Brownian motion, long-range random potential, Lyapunov exponents, shape theorem, large deviations 
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     title = {Large deviations for {Brownian} motion in a random potential},
     journal = {ESAIM: Probability and Statistics},
     pages = {374--398},
     publisher = {EDP-Sciences},
     volume = {24},
     year = {2020},
     doi = {10.1051/ps/2020007},
     mrnumber = {4153636},
     zbl = {1455.82007},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2020007/}
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Boivin, Daniel; Lê, Thi Thu Hien. Large deviations for Brownian motion in a random potential. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 374-398. doi : 10.1051/ps/2020007. http://www.numdam.org/articles/10.1051/ps/2020007/

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