混合随机环境中淬火和退火随机行走的大偏差

Jiaming Chen
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摘要

在这项工作中,我们建立了强混合环境中随机漫步的大偏差原理。淬火率函数和退火率函数具有相同的零集,其形状要么是单点,要么是线段,F.Rassoul-Agha 交流并给出了一个示例。只要控制好无序程度,在混合条件下,两个速率函数在边界的紧凑集上是一致的,而在有限依赖条件下,在内部的紧凑集上也是一致的。沿着这一思路,我们还指出,在略微精细的条件下,两个速率函数的差异存在相变。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Large deviations of quenched and annealed random walk in mixing random environment
In this work, we establish the existence of large deviation principles of random walk in strongly mixing environments. The quenched and annealed rate functions have the same zero set whose shape is either a singleton point or a line segment, with an illustrative example communicated and given by F. Rassoul-Agha. Whenever the level of disorder is controlled, the two rate functions agree on compact set at the boundary under mixing conditions and in the interior under finite-dependence condition. Along the line we also indicate that under slightly more refined conditions, there is a phase transition of the difference of two rate functions.
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