Subhajit Ghosh, Bar-Ilan University, Ramat-Gan, Israel


Mathematics Colloquium

Wednesday, 11 October, 4 pm


Venue: Ramanujan Hall

Host: Murali K. Srinivasan

Speaker: Subhajit Ghosh

Affiliation: Bar-Ilan University, Ramat-Gan, Israel

TITLE: Aldous-type spectral gap results for the complete monomial group

ABSTRACT: Let G be a finite group. We consider a connected graph such that the edges and vertices are equipped with independent Poisson clocks  (alarm clocks that ring at time distributed as the exponential distribution).  Also, there are lamps with configurations indexed by the elements of G and lamplighters at the vertices of the graph.  The lamplighters at a pair of neighboring vertices exchange their position whenever the associated edge rings.  The lamplighter at a vertex updates the lamp configuration whenever the vertex rings.  The process can be viewed as a continuous-time random walk on the complete monomial group G wreath S(n) (symmetric group).   If the configuration of a lamp is x, then it changes to g.x with a non-negative rate alpha(g).  We assume that the rates are symmetric, and the elements g in G with positive alpha(g) generate G.  We show that the spectral gap of the process is the same as that of the continuous-time lamplighter random walk (i.e., the process with a single lamplighter) on the graph.  This is an analog of the Aldous' spectral gap conjecture for the complete monomial group of degree n over G.

Ramanujan Hall, Department of Mathematics
Wed, October 11, 2023
Start Time
4:00pm IST
Created by
Mon, October 9, 2023 1:57pm IST