Fetching the paper…
Reading the bibliography…
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.
λ 1 \lambda_{1} isoperimetric inequalities for graphs, and superconcentrators
N. Alon and V. Milman · 1985
Earlier work this paper cites.
λ 1 \lambda_{1} Eigenvalues and expanders
N. Alon · 1986
Earlier work this paper cites.
Ramanujan Graphs
A. Lubotzky. R. Phillips and P. Sharnak · 1988
Earlier work this paper cites.
Approximate counting, uniform generation and rapidly mixing Markov chains
A. Sinclair and M. Jerrum · 1989
Earlier work this paper cites.
Instability of the Liouville property for quasi-isometric graphs and manifolds of polynomial volume growth
I. Benjamini · 1991
Earlier work this paper cites.
Logarithmic sobolev inequalities for finite markov chains
P. Diaconis and L. Saloff-Coste · 1996
Earlier work this paper cites.
On the stability of the behavior of random walks on groups
C. Pittet and L. Saloff-Coste · 2000
Earlier work this paper cites.
American Institute of Mathematics (AIM) research workshop “Sharp Thresholds for Mixing Times”(Palo Alto, December 2004)
Y. Peres · 2004
Earlier work this paper cites.
Evolving sets, mixing and heat kernel bounds
B. Morris and Y. Peres · 2005
Cited alongside, same era.
Mixing time bounds via the spectral profile
S. Goel, R. Montenegro and P. Tetali · 2006
Cited alongside, same era.
Faster mixing and small bottlenecks
N. Fountoulakis and B. A. Reed · 2007
Cited alongside, same era.
On the precision of the spectral profile
G. Kozma · 2007
Cited alongside, same era.
Markov Chains and Mixing Times
D. Levin, Y. Peres and E. Wilmer · 2009
Cited alongside, same era.
Total variation cutoff in birth-and-death chains
J. Ding, E. Lubetzky and Y. Peres · 2010
Cited alongside, same era.
Explicit expanders with cutoff phenomena
E. Lubetzky and A. Sly · 2011
Comparison of cutoffs between lazy walks and Markovian semigroups
G. Y. Chen and L. Saloff-Coste · 2013
Later among the works it cites.
Sensitivity of mixing times
J. Ding and Y. Peres · 2013
Later among the works it cites.
Mixing times are hitting times of large sets
Y. Peres and P. Sousi · 2013
Later among the works it cites.
Robustness of mixing under rough isometry, via bottleneck sequences
L. Addario-Berry and M. I. Roberts · 2016
Closest in time.
On sensitivity of uniform mixing times
J. Hermon · 2016
Closest in time.
Total Variation and Separation Cutoffs are not equivalent and neither one implies the other
J. Hermon, H. Lacoin and Y. Peres · 2016
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Reversible Markov chains and random walks on graphs
D. Aldous and J. Fill
Cited in the paper.
Closest in time.
Characterization of cutoff for reversible Markov chains
R. Basu, J. Hermon, and Y. Peres · 2017
Closest in time.