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<p>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.</p>

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A Local Limit Theorem for a Random Walk in an Intermittent Dynamical Environment

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  • 发表日期：

    2026年1月14日

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  • Juho Leppänen

摘要

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.