A Notion of Dimension based on Probability on Groups

Abstract: Probability on Groups studies how properties of a group \(G\), such as amenability or growth rate, influence the outcome of random experiments, such as random walk or percolation, carried out on (a Cayley graph of) \(G\). Can we learn something new about \(G\) by studying such experiments? I will survey some results in the area and introduce a notion of “dimension” of a group that arose from the hope to answer this question positively.
https://arxiv.org/abs/2404.17278

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar