Lower bounds for covering times for reversible Markov chains and random walks on graphs

1989 ◽  
Vol 2 (1) ◽  
pp. 91-100 ◽  
Author(s):  
David J. Aldous
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Lower Bounds ◽  
Random Walks On Graphs ◽  
Reversible Markov Chains ◽  
Covering Times

scholarly journals Hitting Times of Walks on Graphs through Voltages

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
José Luis Palacios ◽  
Eduardo Gómez ◽  
Miguel Del Río
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Hitting Times ◽  
Reciprocity Principle ◽  
Triangular Inequality ◽  
Random Walks On Graphs ◽  
Necklace Graph

We derive formulas for the expected hitting times of general random walks on graphs, in terms of voltages, with very elementary electric means. Under this new light we revise bounds and hitting times for birth-and-death Markov chains and for walks on graphs with cutpoints, and give some exact computations on the necklace graph. We also prove Tetali’s formula for hitting times without making use of the reciprocity principle. In fact this principle follows as a corollary of our argument that also yields as corollaries the triangular inequality for effective resistances and the reversibility of the sum of hitting times around a tour.

scholarly journals Limit profiles for reversible Markov chains

2021 ◽  
Author(s):  
Evita Nestoridi ◽  
Sam Olesker-Taylor
Keyword(s):  
Random Walk ◽  
Markov Chains ◽  
Random Walks ◽  
Gibbs Sampler ◽  
Statistical Physics ◽  
Homogeneous Spaces ◽  
New Method ◽  
Reversible Markov Chains ◽  
Similar Approximation ◽  
Random Transpositions

AbstractIn a recent breakthrough, Teyssier (Ann Probab 48(5):2323–2343, 2020) introduced a new method for approximating the distance from equilibrium of a random walk on a group. He used it to study the limit profile for the random transpositions card shuffle. His techniques were restricted to conjugacy-invariant random walks on groups; we derive similar approximation lemmas for random walks on homogeneous spaces and for general reversible Markov chains. We illustrate applications of these lemmas to some famous problems: the k-cycle shuffle, sharpening results of Hough (Probab Theory Relat Fields 165(1–2):447–482, 2016) and Berestycki, Schramm and Zeitouni (Ann Probab 39(5):1815–1843, 2011), the Ehrenfest urn diffusion with many urns, sharpening results of Ceccherini-Silberstein, Scarabotti and Tolli  (J Math Sci 141(2):1182–1229, 2007), a Gibbs sampler, which is a fundamental tool in statistical physics, with Binomial prior and hypergeometric posterior, sharpening results of Diaconis, Khare and Saloff-Coste (Stat Sci 23(2):151–178, 2008).

scholarly journals Coalescent random walks on graphs

2007 ◽  
Vol 202 (1) ◽  
pp. 144-154 ◽  
Author(s):  
Jianjun Paul Tian ◽  
Zhenqiu Liu
Keyword(s):  
Random Walks ◽  
Random Walks On Graphs

scholarly journals Some Inequalities for Reversible Markov Chains

1982 ◽  
Vol s2-25 (3) ◽  
pp. 564-576 ◽  
Author(s):  
David J. Aldous
Keyword(s):  
Markov Chains ◽  
Reversible Markov Chains
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