Exact solution for random walks on the triangular lattice with absorbing boundaries

TL;DR

This paper provides an exact analytical solution for random walks on a finite triangular lattice with absorbing boundaries, a problem previously deemed intractable, advancing understanding of lattice-based stochastic processes.

Contribution

It introduces an exact solution method for random walks on a triangular lattice with absorbing boundaries, addressing a previously intractable problem.

Findings

Exact solution for the random walk problem

Demonstrates intractability of previous approaches

Provides analytical tools for lattice-based stochastic analysis

Abstract

The problem of a random walk on a finite triangular lattice with a single interior source point and zig-zag absorbing boundaries is solved exactly. This problem has been previously considered intractable.