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arXiv · 2609.19115

Singularity of harmonic measure for finitely supported random walks

Petr Kosenko·Giulio Tiozzo
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Abstract

In this paper we affirmatively resolve the singularity conjecture for finitely supported non-degenerate random walks on cocompact Fuchsian groups. The method we use is based on constructing a pair of geodesic currents, one for the Lebesgue measure and one for the random walk measure, and checking that they are different by using Fourier analysis on the boundary.

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Petr Kosenko, Giulio Tiozzo. 2026-09-16. Singularity of harmonic measure for finitely supported random walks. https://arxiv.org/abs/2609.19115

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