Annealed meeting-time analysis for backtracking random walks on locally tree-like graphs

Develop an annealed-law framework to compute the distribution of the first meeting time τ_meet of two independent simple random walks (allowing backtracking) on locally tree-like random graphs (e.g., configuration model or Galton–Watson tree limits), extending current methods that handle non-backtracking walks.

Background

Meeting-time calculations on sparse random graphs are tractable via an annealed exploration procedure when walks are non-backtracking, leveraging local weak limits and unimodular Galton–Watson trees. However, simple random walks backtrack, and the current non-Markovian exploration description does not directly apply.

The authors explicitly highlight the gap for backtracking walks, indicating the need for new ideas to integrate backtracking into the annealed analysis and obtain explicit meeting-time distributions.