The Dirichlet problem at infinity for random walks on graphs with a strong isoperimetric inequality

1992 ◽  
Vol 91 (3-4) ◽  
pp. 445-466 ◽  
Author(s):  
Vadim A. Kaimanovich ◽  
Wolfgang Woess
Keyword(s):  
Dirichlet Problem ◽  
Random Walks ◽  
Isoperimetric Inequality ◽  
Random Walks On Graphs ◽  
Strong Isoperimetric Inequality ◽  
Dirichlet Problem At Infinity

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

On a Result of Aleliunas et al. Concerning Random Walks on Graphs

1990 ◽  
Vol 4 (4) ◽  
pp. 489-492 ◽  
Author(s):  
José Luis Palacios
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Simple Proof ◽  
Hitting Times ◽  
Initial State ◽  
Random Walks On Graphs ◽  
Minimum Number

Aleliunas et al. [3] proved that for a random walk on a connected raph G = (V, E) on N vertices, the expected minimum number of steps to visit all vertices is bounded by 2|E|(N - 1), regardless of the initial state. We give here a simple proof of that result through an equality involving hitting times of vertices that can be extended to an inequality for hitting times of edges, thus obtaining a bound for the expected minimum number of steps to visit all edges exactly once in each direction.

Random Walks on Graphs with Regular Volume Growth

1998 ◽  
Vol 8 (4) ◽  
pp. 656-701 ◽  
Author(s):  
T. Coulhon ◽  
A. Grigoryan
Keyword(s):  
Random Walks ◽  
Volume Growth ◽  
Random Walks On Graphs
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