Open Research Index

birthday-paradox-non-backtracking-regular-graphs

Benjamin Dozier

Palomar Registrypalomar/PALOMAR-2026-10-27-000026Oct 27, 2026math.COscore 0

A Lean 4 and Mathlib formalization (found by Codex GPT 5.6 Sol) of the main theorem of the author's recent arxiv preprint arXiv:2608.26321. This is the Birthday Paradox for non-backtracking walks on regular graphs of degree at least 3: such a walk of length k has high probability of self-intersecting when k is significantly greater than sqrt(n), where n is the number of vertices of the graph. This resolves a conjecture of Noga Alon and Yuval Peres for the fixed degree case.

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