scholarly journals The Branching‐Ruin Number and the Critical Parameter of Once‐Reinforced Random Walk on Trees

2019 ◽  
Vol 73 (1) ◽  
pp. 210-236 ◽  
Author(s):  
Andrea Collevecchio ◽  
Daniel Kious ◽  
Vladas Sidoravicius
Keyword(s):  
Random Walk ◽  
Critical Parameter ◽  
Reinforced Random Walk

scholarly journals Approximating Critical Parameters of Branching Random Walks

2009 ◽  
Vol 46 (02) ◽  
pp. 463-478 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fabio Zucca
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Critical Parameter ◽  
Branching Random Walk ◽  
Critical Parameters ◽  
Bond Percolation ◽  
Branching Random Walks

Given a branching random walk on a graph, we consider two kinds of truncations: either by inhibiting the reproduction outside a subset of vertices or by allowing at most m particles per vertex. We investigate the convergence of weak and strong critical parameters of these truncated branching random walks to the analogous parameters of the original branching random walk. As a corollary, we apply our results to the study of the strong critical parameter of a branching random walk restricted to the cluster of a Bernoulli bond percolation.

Once edge-reinforced random walk on a tree

2002 ◽  
Vol 122 (4) ◽  
pp. 567-592 ◽  
Author(s):  
Rick Durrett ◽  
Harry Kesten ◽  
Vlada Limic
Keyword(s):  
Random Walk ◽  
Reinforced Random Walk

Reinforced random walk

1990 ◽  
Vol 84 (2) ◽  
pp. 203-229 ◽  
Author(s):  
Burgess Davis
Keyword(s):  
Random Walk ◽  
Reinforced Random Walk

scholarly journals Transience of Edge-Reinforced Random Walk

2015 ◽  
Vol 339 (1) ◽  
pp. 121-148 ◽  
Author(s):  
Margherita Disertori ◽  
Christophe Sabot ◽  
Pierre Tarrès
Keyword(s):  
Random Walk ◽  
Reinforced Random Walk
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