Uniform Sampling and Visualization of 3D Reluctant Walks

TL;DR

This paper extends a 2D walk sampling method to 3D, enabling uniform sampling and visualization of constrained walks in the first orthant, facilitating analysis of complex 3D walk behaviors.

Contribution

It introduces a generalized sampler and visualizer for 3D walks confined to the first orthant, handling walks with drift outside the region, which was previously challenging.

Findings

Effective uniform sampling of 3D walks with complex drift.

Visualization tools for 3D walk analysis.

Extension of 2D sampling methods to 3D.

Abstract

A family of walks confined to the first orthant whose defining stepset has drift outside of the region can be challenging to sample uniformly at random for large lengths. We address this by generalizing the 2D walk sampler of Lumbroso et al. to handle 3D walks restricted to the first orthant. The sampler includes a visualizer and means to animate the walks.