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math.PR2026
The maximum relaxation time of a random walk on regular graphs
Haoran Zhu
We establish sharp quadratic bounds on the relaxation time of simple random walk on connected regular graphs, with leading constants and for even and odd orders,…
math.PR2026
Random walks on wreath products and spectral gaps for coloured interchange processes
Haoran Zhu
We introduce group-valued coloured interchange processes, a class of continuous-time random walks on wreath products generated by transpositions and arbitrary symmetric base-group…
math.PR2026
Spectral gap of biased adjacent-transposition chains
Gary R. W. Greaves, Haoran Zhu
We establish a sharp lower bound on the spectral gap of the biased adjacent-transposition Markov chain on the symmetric group. As a consequence, we resolve a longstanding conjectur…