Separation cut-offs for birth and death chains

By Persi Diaconis, L. Saloff‐Coste. 2006

100 citations recorded by the source corpus.

This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions of spectral gap and mixing time. Y. Peres has observed that for many families of Markov chains, there is a cut-off if and only if the product of spectral gap and mixing time tends to infinity. We establish this for arbitrary birth and death chains in continuous time when the convergence is measured in separation and the chains all start at 0.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6663867cf52ea8e7c21c1b4e499d6d6ae8866efa

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In Geometry and Topology

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

On Times to Quasi-stationarity for Birth and Death Processes (2009, methodology): “The corresponding result for discrete time (where exponential laws are replaced by geometric laws for birth and death chains which are monotone and whose associated eigenvalues belong to [0, 1]) is used to build and interpret various stopping times for some irreducible birth and death chains on J0, ”
The Passage Time Distribution for a Birth-and-Death Chain: Strong Stationary Duality Gives a First Stochastic Proof (2007, background): “2 are the starting point of an in-depth consideration of separation cut-off for birth-and-death chains in [6].”
The cutoff phenomenon for ergodic Markov processes (2008, unknown): “The following theorem is proved in [12].”