# On sensitivity of mixing times and cutoff

@inproceedings{Hermon2016OnSO, title={On sensitivity of mixing times and cutoff}, author={Jonathan Hermon and Yuval Peres}, year={2016} }

A sequence of chains exhibits (total-variation) cutoff (resp., pre-cutoff) if for all $0<\epsilon< 1/2$, the ratio $t_{\mathrm{mix}}^{(n)}(\epsilon)/t_{\mathrm{mix}}^{(n)}(1-\epsilon)$ tends to 1 as $n \to \infty $ (resp., the $\limsup$ of this ratio is bounded uniformly in $\epsilon$), where $t_{\mathrm{mix}}^{(n)}(\epsilon)$ is the $\epsilon$-total-variation mixing-time of the $n$th chain in the sequence. We construct a sequence of bounded degree graphs $G_n$, such that the lazy simple random… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

5

Twitter Mentions

#### Citations

##### Publications citing this paper.

SHOWING 1-8 OF 8 CITATIONS

## A comparison principle for random walk on dynamical percolation.

VIEW 4 EXCERPTS

CITES BACKGROUND

## PR ] 7 F eb 2 01 9 Random walk on dynamical percolation

VIEW 4 EXCERPTS

CITES BACKGROUND

## Statement of research

VIEW 7 EXCERPTS

CITES BACKGROUND

## Perfect Sampling for Quantum Gibbs States

VIEW 3 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Maximal Inequalities and Mixing Times

VIEW 3 EXCERPTS

CITES BACKGROUND

## On sensitivity of uniform mixing times

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 22 REFERENCES

## Sensitivity of mixing times

VIEW 8 EXCERPTS

## Comparison of Cutoffs Between Lazy Walks and Markovian Semigroups

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## On the stability of the behavior of random walks on groups

VIEW 8 EXCERPTS

HIGHLY INFLUENTIAL

## On sensitivity of uniform mixing times

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Explicit Expanders with Cutoff Phenomena

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Characterization of cutoff for reversible Markov chains

VIEW 3 EXCERPTS

## Mixing Times are Hitting Times of Large Sets

VIEW 1 EXCERPT

## Markov Chains and Mixing Times

VIEW 1 EXCERPT