Author

P. Kosenko

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Preprint Sep 2026

Singularity of harmonic measure for finitely supported random walks

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...

P. Kosenko, Giulio Tiozzo · 1 citation · ⚡1

Preprint Oct 2026

Point Configurations in Brownian Traces

We study finite and countable point configurations in the trace of Brownian motion in $\mathbb{R}^d$, $d\geq2$. In the plane, the set of translations placing a prescribed finite configuration on the trace has Hausdorff dimension two in every nonempty open set; we prove analogous dimension-preservation results for radia...

P. Kosenko, J. M. Medina, A. Yavicoli · 0 citations