{"ID":22994682,"CreatedAt":"2026-09-17T04:01:24.020413181Z","UpdatedAt":"2026-09-17T04:01:24.020413181Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19115","arxiv_id":"2609.19115","title":"Singularity of harmonic measure for finitely supported random walks","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.","short_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 differen...","url_abs":"https://arxiv.org/abs/2609.19115","url_pdf":"https://arxiv.org/pdf/2609.19115v1","authors":"[\"Petr Kosenko\",\"Giulio Tiozzo\"]","published":"2026-09-16T17:41:42Z","proceeding":"math.DS","tasks":"[\"math.DS\",\"math.PR\"]","methods":"[]","has_code":false}