Submission date: 16 June 2022

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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Full text arXiv 2206.08276: pdf, ps.