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In this note, we demonstrate an instance of bounded-degree graphs of size $n$, for which the total variation mixing time for the random walk is decreased by a factor of $\log n/ \log\log n$ if we multiply the edge-conductances by bounded factors in a certain way.
Rapid convergence to equilibrium of stochastic Ising models in the Dobrushin Shlosman regime
M. Aizenman and R. Holley · 1987
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Instability of the Liouville property for quasi-isometric graphs and manifolds of polynomial volume growth
I. Benjamini · 1991
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Logarithmic Sobolev inequalities for finite Markov chains
P. Diaconis and L. Saloff-Coste · 1996
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Faster mixing via average conductance
L. Lovász and R. Kannan · 1999
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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.
Reversible Markov Chains and Random Walks on Graphs
D. Aldous and J. Fill
Cited in the paper.
The mixing time of the giant component of a random graph
I. Benjamini, G. Kozma, and N. C. Wormald
Cited in the paper.
Mixing times are hitting times of large sets
Y. Peres and P. Sousi
Cited in the paper.
The evolution of the mixing rate of a simple random walk on the giant component of a random graph
N. Fountoulakis and B. A. Reed · 2008
Later among the works it cites.
Critical random graphs: diameter and mixing time
A. Nachmias and Y. Peres · 2008
Later among the works it cites.
Markov chains and mixing times
D. A. Levin, Y. Peres, and E. L. Wilmer · 2009
Later among the works it cites.
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