Stationary probability of the identity for the TASEP on a Ring
2012 (English)Other (Other academic)
Consider the following Markov chain on permutations of length n. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap positions. Otherwise nothing happens, corresponding to a loop in the Markov chain. This is the circular TASEP. We compute the average proportion of time the chain spends at the identity permutation (and, in greater generality, at sorted words). This answers a conjecture by Thomas Lam.
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IdentifiersURN: urn:nbn:se:kth:diva-156857OAI: oai:DiVA.org:kth-156857DiVA: diva2:768228
QC 201412032014-12-032014-12-032014-12-04Bibliographically approved