Topic: Random Walks in Higher Dimensions

The Fourier Symbol of a Simple Symmetric Walk

Return-Probability Asymptotics from Fourier Analysis

Periodicity and Even-Time Returns on the Lattice

Pólya’s Theorem from the Green Function

Numerical Green-Function Integrals and Cutoff Diagnostics

Nearest-Neighbor Walks on the Integer Lattice

Logarithmic Green-Function Divergence in Two Dimensions

Local Integrability at the Singular Point

Lazy Walks and Recurrence Classification

Green Functions and Expected Visit Counts