Multiplicative structures and random walks in o-minimal groups

2022/06/16 by Spink, Hunter · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO) #Probability (math.PR)

paper · doi:10.48550/arxiv.2206.08276

Abstract

We prove structure theorems for o-minimal definable subsets S⊂ G of definable groups containing large multiplicative structures, and show definable groups do not have bounded torsion arbitrarily close to the identity. As an application, for certain models of n-step random walks X in G we show upper bounds ℙ(X∈ S)≤ n^-C and a structure theorem for the steps of X when ℙ(X∈ S)≥ n^-C'.

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• Uniform spectral gaps, non-abelian Littlewood-Offord and anti-concentration for random walks

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