A Spanning Tree Method for Bounding Hitting Times of Random Walks on Graphs

2010 ◽  
Vol 24 (3) ◽  
pp. 808-820 ◽  
Author(s):  
Randy Cogill ◽  
Cheng Peng
Keyword(s):  
Random Walks ◽  
Spanning Tree ◽  
Hitting Times ◽  
Random Walks On Graphs ◽  
Tree Method

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.

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 First hitting times of simple random walks on graphs with congestion points

2003 ◽  
Vol 2003 (30) ◽  
pp. 1911-1922 ◽  
Author(s):  
Mihyun Kang
Keyword(s):  
Random Walks ◽  
Generating Functions ◽  
Hitting Times ◽  
Group Representations ◽  
Explicit Formulas ◽  
Probability Generating Functions ◽  
Random Walks On Graphs ◽  
First Hitting Times

We derive the explicit formulas of the probability generating functions of the first hitting times of simple random walks on graphs with congestion points using group representations.

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
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