Minimal thinness with respect to symmetric L\'evy processes

TL;DR

This paper develops criteria to determine when a set is minimally thin at boundary points for a broad class of symmetric Lévy processes, enhancing understanding of boundary behavior in potential theory.

Contribution

It introduces new tests for minimal thinness at boundary points specific to symmetric Lévy processes, expanding the theoretical framework.

Findings

Provided criteria for minimal thinness at finite boundary points

Extended tests to infinite boundary points

Applicable to a large class of purely discontinuous symmetric Lévy processes

Abstract

Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness at finite and infinite minimal Martin boundary points for a large class of purely discontinuous symmetric L\'evy processes.