Strict comparison for the Lyapunov exponents of the simple random walk in random potentials

2020/10/17 by Naoki Kubota, Kubota, Naoki
Mathematics · Physics and Astronomy · #60E15 #60F10 #60K37 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2010.08798

openalex publication_date 2020/10/17 · openalex created_date 2020/10/22 · openalex updated_date 2026/08/04

Abstract

We consider the simple random walk in i.i.d. nonnegative potentials on the d-dimensional cubic lattice ℤ^d (d ≥ 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.

Citations

• Moderate deviations for the chemical distance in Bernoulli percolation
• Continuity of the time and isoperimetric constants in supercritical\n percolation

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