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

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 Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ryuya Namba
Keyword(s):  
Random Walks ◽  
Quadratic Forms ◽  
Volume Growth ◽  
Moderate Deviation ◽  
Point Of View ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
Geometric Point ◽  
Rate Functions ◽  
The Given

AbstractModerate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.

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.

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