For reversible finite Markov chains, the L-infinity mixing time is at most trel log(e thit / trel), so the mixing time is comparable to the maximal hitting time exactly when the spectral gap times the hitting time remains bounded; this resolves the Aldous-Fill coalescence conjecture under…
Sensitivity of mixing times of Cayley graphs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We show that the total variation mixing time is not quasi-isometry invariant, even for Cayley graphs. Namely, we construct a sequence of pairs of Cayley graphs with maps between them that twist the metric in a bounded way, while the ratio of the two mixing times goes to infinity. The Cayley graphs serving as an example have unbounded degrees. For non-transitive graphs we construct bounded degree graphs for which the mixing time from the worst starting point for one graph is asymptotically smaller than the mixing time from the best starting point of the random walk on a network obtained by increasing some of the edge weights from 1 to $1+o(1)$.
fields
math.PR 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Some inequalities for reversible Markov chains and branching random walks via spectral optimization
For reversible finite Markov chains, the L-infinity mixing time is at most trel log(e thit / trel), so the mixing time is comparable to the maximal hitting time exactly when the spectral gap times the hitting time remains bounded; this resolves the Aldous-Fill coalescence conjecture under…