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ID 14929
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Abstract
In 1993, Menshikov and Zuev introduced ρ−percolation model, in which a path of a graph is ρ−passable in a bond percolation configuration if the concentration of open bonds on it is at least ρ, and concerning this model, they gave four open problems. In this paper, we answer three problems out of them : the first one is whether the ρ−percolation critical probability is equal to the critical probability corresponding to finite/infinite expectation of the number of ρ−connectable vertices from a fixed vertex, the second is whether the 1-p ercolation critical probability is equal to the Bernoulli bond percolation critical probability, and finally the third is whether the probability of the existence of ρ−passable path of length exceeding n starting from a fixed vertex always decays exponentially in the subcritical phase.
Publication Title
岡山大学経済学会雑誌
Published Date
2009-03-10
Volume
volume40
Issue
issue4
Publisher
岡山大学経済学会
Publisher Alternative
The economic association of okayama university
Start Page
115
End Page
125
ISSN
0386-3069
NCID
AN00032897
Content Type
Journal Article
Related Url
http://www.e.okayama-u.ac.jp/~shiryou/gakkaishi.htm
OAI-PMH Set
岡山大学
language
英語
Copyright Holders
岡山大学経済学会
File Version
publisher
NAID
Eprints Journal Name
oer