# Boundary behavior for random walks in cones

## TL;DR

This paper investigates how zero-drift random walks behave near the boundaries of convex cones, providing a local limit theorem that describes their asymptotic distribution in this regime.

## Contribution

It introduces a local limit theorem for zero-drift random walks in convex cones near the boundary, advancing understanding of their boundary behavior.

## Key findings

- Derived a local limit theorem for boundary behavior
- Characterized asymptotic distribution near cone boundaries
- Enhanced theoretical understanding of constrained random walks

## Abstract

We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.