Multiplicative structures and random walks in o-minimal groups

Hunter Spink

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arXiv · 2206.08276

Multiplicative structures and random walks in o-minimal groups

Hunter Spink

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Abstract

We prove structure theorems for o-minimal definable subsets $S\subset G$ 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 $\mathbb{P}(X\in S)\le n^{-C}$ and a structure theorem for the steps of $X$ when $\mathbb{P}(X\in S)\ge n^{-C'}$.

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BibTeX RIS

Hunter Spink. 2022-06-16. Multiplicative structures and random walks in o-minimal groups. https://arxiv.org/abs/2206.08276

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