Mixing Times are Hitting Times of Large Sets
By Yuval Peres, Perla Sousi. 2011
110 citations recorded by the source corpus.
We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. We relate them by showing that the mixing time of the lazy chain is equivalent to the maximum over initial states $$x$$x and large sets $$A$$A of the hitting time of $$A$$A starting from $$x$$x. We also prove that the first time when averaging over two consecutive time steps is close to stationarity is equivalent to the mixing time of the lazy version of the chain.
Subfields: Computational Theory and Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/0a7a5b12e4c1fe57c3f5c00e5386f7d054fb9acb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Statistics and Probability
- Roberto Imbuzeiro Oliveira
- Joel A. Tropp
- Stanislav Minsker
- Per-Gunnar Martinsson
- T. Von
- Ramon van Handel
- Qiang Zeng
- Marius Junge
Citations in the corpus
- Mixing and hitting times for finite Markov chains (2011, background): “sOther applications of (slight variants of) our theorems are considered in [8].”