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For birth and death chains, we derive bounds on the spectral gap and mixing time in terms of birth and death rates.
Hardy’s inequality with weights
Benjamin Muckenhoupt · 1972
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Random walks on finite groups and rapidly mixing Markov chains
David Aldous · 1983
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Identifying coefficients in the spectral representation for first passage time distributions
M. Brown and Y.-S. Shao · 1987
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Group representations in probability and statistics
Persi Diaconis · 1988
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Geometric bounds for eigenvalues of Markov chains
Persi Diaconis and Daniel Stroock · 1991
Earlier work this paper cites.
Comparison techniques for random walk on finite groups
Persi Diaconis and Laurent Saloff-Coste · 1993
Earlier work this paper cites.
Comparison theorems for reversible Markov chains
Persi Diaconis and Laurent Saloff-Coste · 1993
Cited alongside, same era.
The cutoff phenomenon in finite Markov chains
Persi Diaconis · 1996
Cited alongside, same era.
What do we know about the Metropolis algorithm?
P. Diaconis and L. Saloff-Coste · 1998
Cited alongside, same era.
An example of application of discrete Hardy’s inequalities
L. Miclo · 1999
Cited alongside, same era.
Simple examples of the use of Nash inequalities for finite Markov chains
L. Saloff-Coste · 1999
Cited alongside, same era.
The cutoff phenomenon for finite Markov chains
Guan-Yu Chen · 2006
Cited alongside, same era.
Separation cut-offs for birth and death chains
Persi Diaconis and Laurent Saloff-Coste · 2006
Later among the works it cites.
The cutoff phenomenon for ergodic markov processes
Guan-Yu Chen and Laurent Saloff-Coste · 2008
Later among the works it cites.
Abrupt convergence and escape behavior for birth and death chains
J. Barrera, O. Bertoncini, and R. Fernández · 2009
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Total variation cutoff in birth-and-death chains
Jian Ding, Eyal Lubetzky, and Yuval Peres · 2010
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Comparison of cutoffs between lazy walks and markovian semigroups
Guan-Yu Chen and Laurent Saloff-Coste · 2012
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Spectral computations for birth and death chains
Guan-Yu Chen and Laurent Saloff-Coste · 2012
Later among the works it cites.
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