We provide a general framework for computing mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary distributions of finite Markov chains. We introduce a new Markov chain on linear extensions of a poset with n vertices, which is a variant of the promotion Markov chain of Ayyer, Klee and the last author, and show that it has a mixing time O(n log n).
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Mixing time for Markov chain on linear extensions
We provide a general framework for computing mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary distributions of finite Markov chains. We introduce a new Markov chain on linear extensions of a poset with n vertices, which is a variant of the promotion Markov chain of Ayyer, Klee and the last author, and show that it has a mixing time O(n log n).
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 NSFPAR ID:
 10287170
 Date Published:
 Journal Name:
 Séminaire lotharingien de combinatoire
 Volume:
 85B
 ISSN:
 12864889
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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