论文标题
简单随机步行的Lyapunov指数的严格比较
Strict comparison for the Lyapunov exponents of the simple random walk in random potentials
论文作者
论文摘要
我们考虑I.I.D.中简单的随机步行$ d $ d $二维立方晶格$ \ mathbb {z}^d $（$ d \ geq 1 $）上的非负潜力。在此模型中，所谓的Lyapunov指数描述了潜在的简单随机行走的旅行成本。 Lyapunov指数取决于电势的分布函数，本文的目的是证明Lyapunov指数严格在电势的分布函数中是单调的，该命令是根据严格的优势。此外，Lyapunov指数的比较还提供了该模型速率函数的比较。
We consider the simple random walk in i.i.d. nonnegative potentials on the $d$-dimensional cubic lattice $\mathbb{Z}^d$ ($d \geq 1$). In this model, the so-called Lyapunov exponent describes the cost of traveling for the simple random walk in the potential. The Lyapunov exponent depends on the distribution function of the potential, and the aim of this article is to prove that the Lyapunov exponent is strictly monotone in the distribution function of the potential with the order according to strict dominance. Furthermore, the comparison for the Lyapunov exponent also provides that for the rate function of this model.
