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
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Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)