随机势中布朗运动的大偏差

Pub Date : 2020-01-01 DOI:10.1051/ps/2020007

D. Boivin, Thi Thu Hien Lê

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引用次数: 1

摘要

证明了静止势下布朗运动的淬灭大偏差原理。由于证明是基于Sznitman [Comm. Pure apple]开发的一种方法。数学[j] . 47(1994)[1655-1688]对于有紧支承的障碍物之间的布朗运动，不需要势的正则性条件。特别是，充分条件由多项式衰减相关的势来验证，如帕斯图尔[Teoret]研究的经典势。[J] .科学通报，2002(2):1 - 8。物理学报，133(2008)639-657]和Lacoin最近介绍的电位[Ann。亨利·庞卡罗:可能吧。Stat. 48 (2012) 1010-1028;1029 - 1048年)。

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Large deviations for Brownian motion in a random potential

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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