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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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Normal distributions of finite Markov chains
We show that the stationary distribution of a finite Markov chain can be expressed as the sum of certain normal distributions. These normal distributions are associated to planar graphs consisting of a straight line with attached loops. The loops touch only at one vertex either of the straight line or of another attached loop. Our analysis is based on our previous work, which derives the stationary distribution of a finite Markov chain using semaphore codes on the Karnofsky–Rhodes and McCammond expansion of the right Cayley graph of the finite semigroup underlying the Markov chain.
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- PAR ID:
- 10148320
- Date Published:
- Journal Name:
- International Journal of Algebra and Computation
- Volume:
- 29
- Issue:
- 08
- ISSN:
- 0218-1967
- Page Range / eLocation ID:
- 1431 to 1449
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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).more » « less
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1142/S0218196719500577
