Aldous-type spectral gap results for the complete monomial group

2023/09/21 by Subhajit Ghosh, Ghosh, Subhajit
Computer Science · Mathematics · Physics and Astronomy · #05C50 #15A18 #20C15 #37A30 #60J27 #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2309.12154

openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let us consider the continuous-time random walk on G\wr S_n, the complete monomial group of degree n over a finite group G, as follows: An element in G\wr S_n can be multiplied (left or right) by an element of the form \beginitemize \item (u,v)_G:=(e,…,e;(u,v)) with rate x_u,v(≥ 0), or \item (g)^(w):=(…,e,\hspace*-0.65cm\underset\substack\uparrow wth positiong\hspace*-0.65cm,e,…;id) with rate y_wα_g (y_w> 0, α_g=α_g^-1≥ 0), \enditemize such that \(u,v)_G, (g)^(w):x_u,v>0, y_wα_g>0, 1≤ u

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