### Realizations of random walk entropy

Probability Seminar

3rd November 2021, 4:00 pm – 5:00 pm

Fry Building, G.07 (also on zoom)

Random walk entropy is a numerical measure of the behaviour of the random walk at infinity. Out of all random walks on groups generated by d elements, the free group has the maximal entropy. One may ask naturally which intermediate values between 0 and the full entropy of the free group can be realized as entropies of random walks on groups. This question is still open.

We analyze a related question, which is a "stochastic" version of the above open question.

Here we are able to provide a full answer for quotients of the free group, and even a bit further than that.

Generalizing results of Bowen (Inventiones 2014), we show that all possible "IRS entropy" values can be realized on the free group.

These notions will be precisely explained during the talk.

Based on joint works with Yair Hartman and Liran Ron-George.

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