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Limit profiles for Markov chains, part 1
Diaconis and Shahshahani studied the random transpositions shuffle; pick two cards uniformly at random and swap them. They introduced a Fourier analysis technique to prove that it takes $1/2 n \log n$ steps to shuffle a deck of $n$ cards this way. More recently, Teyssier extended this technique to study the exact shape of the total variation distance of the transition matrix from the stationary measure at the cutoff time, giving rise to the notion of a limit profile.
In this talk, we will present a technique that allows one to study the limit profile of star transpositions, which turns out to have the same limit profile as random transpositions, and discuss open questions on the limit profile for card shuffles.
In the second talk, we focus on limit profiles for exclusion processes. Very recently, Bufetov and Nejjar determined the limit profile of the asymmetric simple exclusion process using random walks on Hecke algebras. We discuss how the limit profile can be obtained for the asymmetric simple exclusion process with one open boundary. This is based on joint work with Jimmy He.
Evita Nestoridi
2024.05.13 14.00 GMT+1 (15.00 CEST)
Limit profiles of Markov chains, part 2
In this second part of the talk, we focus on limit profiles for exclusion processes. Very recently, Bufetov and Nejjar determined the limit profile of the asymmetric simple exclusion process using random walks on Hecke algebras. We discuss how the limit profile can be obtained for the asymmetric simple exclusion process with one open boundary. This is based on joint work with Jimmy He.
Dominik Schmid
2024.05.13 15.00 GMT+1 (16.00 CEST)
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