Random Walks on Weighted Graphs of Groups

2019 ◽  
pp. 141-154
Author(s):  
Anne Broise-Alamichel ◽  
Jouni Parkkonen ◽  
Frédéric Paulin
Keyword(s):  
Random Walks ◽  
Weighted Graphs ◽  
Graphs Of Groups

scholarly journals Critical Behaviors and Critical Values of Branching Random Walks on Multigraphs

2008 ◽  
Vol 45 (02) ◽  
pp. 481-497 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fabio Zucca
Keyword(s):  
Random Walks ◽  
Large Class ◽  
Geometric Parameter ◽  
Critical Value ◽  
Critical Values ◽  
Regular Graphs ◽  
Weighted Graphs ◽  
Bounded Degree ◽  
Branching Random Walks ◽  
Weak Phase

We consider weak and strong survival for branching random walks on multigraphs with bounded degree. We prove that, at the strong critical value, the process dies out locally almost surely. We relate the weak critical value to a geometric parameter of the multigraph. For a large class of multigraphs (which enlarges the class of quasi-transitive or regular graphs), we prove that, at the weak critical value, the process dies out globally almost surely. Moreover, for the same class, we prove that the existence of a pure weak phase is equivalent to nonamenability. The results are extended to branching random walks on weighted graphs.

scholarly journals LOCALIZATION ON SNOWFLAKE DOMAINS

Fractals ◽  
2007 ◽  
Vol 15 (03) ◽  
pp. 255-272 ◽  
Author(s):  
BRITTA DAUDERT ◽  
MICHEL L. LAPIDUS
Keyword(s):  
Random Walks ◽  
Geometric Features ◽  
Weighted Graphs ◽  
Narrow Channels ◽  
Koch Snowflake ◽  
Grid Points ◽  
Localization Of Eigenfunctions

The geometric features of the square and triadic Koch snowflake drums are compared using a position entropy defined on the grid points of the discretizations (prefractals) of the two domains. Weighted graphs using the geometric quantities are created and random walks on the two prefractals are performed. The aim is to understand if the existence of narrow channels in the domain may cause the "localization" of eigenfunctions.

scholarly journals Spanning trees and random walks on weighted graphs

2015 ◽  
Vol 273 (1) ◽  
pp. 241-255 ◽  
Author(s):  
Xiao Chang ◽  
Hao Xu ◽  
Shing-Tung Yau
Keyword(s):  
Random Walks ◽  
Spanning Trees ◽  
Weighted Graphs

scholarly journals Critical Behaviors and Critical Values of Branching Random Walks on Multigraphs

2008 ◽  
Vol 45 (2) ◽  
pp. 481-497 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fabio Zucca
Keyword(s):  
Random Walks ◽  
Large Class ◽  
Geometric Parameter ◽  
Critical Value ◽  
Critical Values ◽  
Regular Graphs ◽  
Weighted Graphs ◽  
Bounded Degree ◽  
Branching Random Walks ◽  
Weak Phase

We consider weak and strong survival for branching random walks on multigraphs with bounded degree. We prove that, at the strong critical value, the process dies out locally almost surely. We relate the weak critical value to a geometric parameter of the multigraph. For a large class of multigraphs (which enlarges the class of quasi-transitive or regular graphs), we prove that, at the weak critical value, the process dies out globally almost surely. Moreover, for the same class, we prove that the existence of a pure weak phase is equivalent to nonamenability. The results are extended to branching random walks on weighted graphs.

Random walks on weighted graphs and applications to on-line algorithms

1993 ◽  
Vol 40 (3) ◽  
pp. 421-453 ◽  
Author(s):  
Don Coppersmith ◽  
Peter Doyle ◽  
Prabhakar Raghavan ◽  
Marc Snir
Keyword(s):  
Random Walks ◽  
Weighted Graphs ◽  
On Line
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