Scholarlink

<p>We consider a random walk in an independent and identically distributed (i.i.d.) random environment on ℤ<sup><i>d</i></sup> and study properties of its large deviation rate function at the origin. It was proved by Comets, Gantert and Zeitouni in dimension <i>d</i> = 1 in 1999 and later by Varadhan in dimensions <i>d</i> ≥ 2 in 2003 that, for uniformly elliptic i.i.d. random environments, the quenched and the averaged large deviation rate functions coincide at the origin. Here we provide a description of an atypical event realizing the correct quenched large deviation rate in the nestling and marginally nestling setting: the random walk seeks regions of space where the environment emulates the element in the convex hull of the support of the law of the environment at a site which minimizes the rate function. Periodic environments play a natural role in this description.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Large Deviations at the Origin of Random Walk in Random Environment

  • 期刊论文

  • 发表日期：

    2026年6月15日

查看全文
  • Alexander Drewitz,
  • Alejandro Ramírez,
  • Santiago Saglietti,
  • Zhicheng Zheng

摘要

We consider a random walk in an independent and identically distributed (i.i.d.) random environment on ℤd and study properties of its large deviation rate function at the origin. It was proved by Comets, Gantert and Zeitouni in dimension d = 1 in 1999 and later by Varadhan in dimensions d ≥ 2 in 2003 that, for uniformly elliptic i.i.d. random environments, the quenched and the averaged large deviation rate functions coincide at the origin. Here we provide a description of an atypical event realizing the correct quenched large deviation rate in the nestling and marginally nestling setting: the random walk seeks regions of space where the environment emulates the element in the convex hull of the support of the law of the environment at a site which minimizes the rate function. Periodic environments play a natural role in this description.