Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 59 min ago
PreprintarXiv licencearXiv

Singularity of harmonic measure for finitely supported random walks

  • Petr Kosenko
  • Giulio Tiozzo
Open at sourcePDFDOICite

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.

Related

  1. Singularity of harmonic measure on Poisson--Voronoi tessellations in hyperbolic spaces
    Kohki Sakamoto
    arXivPreprintarXiv licenceFull textDynamical systemsProbabilityarXiv
  2. Conditioned random walks on linear groups I: construction of the target harmonic measure
    Ion Grama, Jean-François Quint, Hui Xiao
    Probability Theory and Related FieldsPeer-reviewedLicence not statedFull textMathematical physicsHAL
  3. Convergence of the Sinkhorn Riemannian metric for finitely supported measures
    Gilles Mordant, Liane Xu
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  4. Finite Dependence and Invariance Hierarchies for Finitely Supported Structures
    Gabriel Ciobanu
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryLogic & foundationsarXiv
  5. Analytic inverse problems with finitely many random measurements
    Giovanni S. Alberti, Damiano Poletti, Simone Sanna +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@misc{kosenko2026singularity,
  title = {{Singularity of harmonic measure for finitely supported random walks}},
  author = {Petr Kosenko and Giulio Tiozzo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19115},
  eprint = {2609.19115},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19115},
}
RIS
TY  - UNPB
TI  - Singularity of harmonic measure for finitely supported random walks
AU  - Petr Kosenko
AU  - Giulio Tiozzo
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19115
UR  - https://arxiv.org/abs/2609.19115
AB  - 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.
ER  -