A local limit theorem for a random walk in an intermittent dynamical environment

Juho Leppänen

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arXiv · 2509.15158

A local limit theorem for a random walk in an intermittent dynamical environment

Juho Leppänen

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Abstract

We study an extended dynamical system on the non-negative real line with piecewise linear non-uniformly expanding local dynamics. With a uniformly distributed initial state, the distribution of successive states coincides with that of a random walk in an inhomogeneous environment. Under suitable conditions on the environment, we establish a central limit theorem and a (non-Gaussian) local limit theorem for the walk. Our approach builds on the work of Leskelä and Stenlund (Stochastic Process. Appl. 121(12), 2011), who analyzed a corresponding model with uniformly expanding local dynamics.

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Juho Leppänen. 2026-01-08. A local limit theorem for a random walk in an intermittent dynamical environment. https://arxiv.org/abs/2509.15158

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