A Local Limit Theorem for a Random Walk in an Intermittent Dynamical Environment
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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Stochastic processes and statistical mechanics
Probability and Statistical Research
Publication details
- Journal / source
- Journal of Theoretical Probability
- Volume
- 39
- Issue
- 1
- Publication date
- 14 January 2026
- Language
- EN