Aperiodic random walks: uniform estimates, local limits and invariance principles

Jiaming Xu

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arXiv · 2609.02257

Aperiodic random walks: uniform estimates, local limits and invariance principles

Jiaming Xu

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Abstract

We prove uniform endpoint estimates, killed local limits, and conditioned-bridge invariance principles for triangular arrays of centered, aperiodic, integer-valued random walks with uni- form exponential tails. The endpoint estimates cover all nonnegative heights, while the local limits treat positive diffusive and zero endpoints. The increment law may vary with the scaling parameter.

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Jiaming Xu. 2026-09-02. Aperiodic random walks: uniform estimates, local limits and invariance principles. https://arxiv.org/abs/2609.02257

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