论文标题
形状定理和一个随机势能淬灭的Lyapunov指数的变异公式
A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential
论文作者
论文摘要
我们证明了一个形状定理，并得出了限制淬灭Lyapunov指数的变异公式，以及在任意维度和任意有限的步骤中的正方形晶格上随机势能以随机势的绿色随机行走功能。潜力是固定环境和步行步骤的函数。这种潜力可能会构成瞬间假设，其严格性与环境的混合有关。我们的设置包括定向和无向聚合物，在静态和动态的随机环境中随机行走，当温度降至零时，我们的结果还提供了形状定理和一个变异公式，用于位点常数和边缘的最后一个通用渗透和标准的第一阶段渗透。
We prove a shape theorem and derive a variational formula for the limiting quenched Lyapunov exponent and the Green's function of random walk in a random potential on a square lattice of arbitrary dimension and with an arbitrary finite set of steps. The potential is a function of a stationary environment and the step of the walk. This potential is subject to a moment assumption whose strictness is tied to the mixing of the environment. Our setting includes directed and undirected polymers, random walk in static and dynamic random environment, and, when the temperature is taken to zero, our results also give a shape theorem and a variational formula for the time constant of both site and edge directed last-passage percolation and standard first-passage percolation.
