Cut-off and Escape Behaviors for Birth and Death Chains on Trees

Olivier Bertoncini · arXiv (Cornell University) · 2010

Summary

Families of discrete time birth and death chains on trees are considered, and it is shown that in presence of a drift towards the root of the tree, the chains exhibit cut-off behavior along the drift and escape behavior in the opposite direction.

Type: preprint
Published: 2010-06-22
Cited by: 1
References: 15
Access: Open access
DOI: https://doi.org/10.48550/arxiv.1006.4324
arXiv: https://arxiv.org/abs/1006.4324
OpenAlex: https://openalex.org/W1795569644
Semantic Scholar: https://api.semanticscholar.org/CorpusID:15474274

Keywords

Root (linguistics), Tree (set theory), Family tree, Statistical physics, Physics

References

Lectures on Complex NetworksS. N. Dorogovt︠s︡ev — 2010
Denumerable Markov chainsJohn G. Kemeny, J. Laurie Snell, Anthony W. Knapp — 1969
Denumerable Markov Chains: Generating Functions, Boundary Theory, Random Walks on TreesWolfgang Woess — 2009
Convergence abrupte et métastabilitéOlivier Bertoncini — 2007
Metastable behavior of stochastic dynamics: A pathwise approachM. Cassandro, Antonio Galves, Enzo Olivieri — 1984
Critical phenomena in complex networksS. N. Dorogovt︠s︡ev, A. V. Goltsev, J. F. F. Mendes — 2007
Random Walks and Percolation on TreesRussell Lyons — 1990
Cut-off and exit from metastability: two sides of the same coinOlivier Bertoncini, Javiera Barrera, Roberto Fernández — 2008
Abrupt Convergence and Escape Behavior for Birth and Death ChainsJ. Barrera, O. Bertoncini, R. Fernández — 2009
SHUFFLING CARDS AND STOPPING-TIMESDavid Aldous, Persi Diaconis — 1986
Decay rates and cutoff for convergence and hitting times of Markov chains with countably infinite state spaceServet Martı́nez, Bernard Ycart — 2001
Strong uniform times and finite random walksDavid Aldous, Persi Diaconis — 1987
The cutoff phenomenon for ergodic Markov processesGuan‐Yu Chen, Laurent Saloff‐Coste — 2008
Random walks on finite groups and rapidly mixing markov chainsD. Aldous — 1983

Cited by

Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting TimesJosé Luis Palacios, Daniel A. Quiroz — 2015

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