TL;DR
Return Probability of Random Walks by Dimension: A canonical quantitative trading interview question at olympiad difficulty. Commonly asked at Jane Street, Two Sigma, DE Shaw.
By Valenke Exam Prep Team·Last updated 2026-06-01
olympiadMarkov Chains & Random Walks
Return Probability of Random Walks by Dimension
Asked at: Jane Street, Two Sigma, DE Shaw
Problem
A symmetric random walk on starts at the origin. In 1D and 2D, the walk returns to the origin with probability 1 (Pólya's theorem). In 3D, the return probability is strictly less than 1. Compute the return probability for .
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