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Differences between Lyapunov exponents for the simple random walk in Bernoulli potentials
- Part of
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- Journal:
- Journal of Applied Probability / Volume 61 / Issue 1 / March 2024
- Published online by Cambridge University Press:
- 23 June 2023, pp. 82-103
- Print publication:
- March 2024
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- Article
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We consider the simple random walk on the d-dimensional lattice
$\mathbb{Z}^d$ (
$d \geq 1$), traveling in potentials which are Bernoulli-distributed. The so-called Lyapunov exponent describes the cost of traveling for the simple random walk in the potential, and it is known that the Lyapunov exponent is strictly monotone in the parameter of the Bernoulli distribution. Hence the aim of this paper is to investigate the effect of the potential on the Lyapunov exponent more precisely, and we derive some Lipschitz-type estimates for the difference between the Lyapunov exponents.
