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Random walks and the regeneration time
Author(s) -
Beveridge Andrew,
Lovász László
Publication year - 1998
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199810)29:2<57::aid-jgt1>3.0.co;2-b
Subject(s) - random walk , mathematics , combinatorics , undirected graph , graph , discrete mathematics , random graph , distribution (mathematics) , stopping time , statistics , mathematical analysis
Consider a graph G and a random walk on it. We want to stop the random walk at certain times (using an optimal stopping rule) to obtain independent samples from a given distribution ρ on the nodes. For an undirected graph, the expected time between consecutive samples is maximized by a distribution equally divided between two nodes, and so the worst expected time is 1/4 of the maximum commute time between two nodes. In the directed case, the expected time for this distribution is within a factor of 2 of the maximum. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 57–62, 1998