Log-concavity in planar random walks

TL;DR

This paper proves that the probabilities of a lattice random walk exiting specific planar regions follow a log-concave distribution, providing new insights into the probabilistic behavior of such walks.

Contribution

The paper introduces a novel proof of log-concavity for exit probabilities of planar lattice random walks, expanding understanding of their probabilistic structure.

Findings

Exit probabilities are log-concave in certain planar regions

Log-concavity holds for a class of lattice random walks

Provides a new theoretical framework for analyzing random walk exit probabilities

Abstract

We prove log-concavity of exit probabilities of lattice random walks in certain planar regions.