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math.PR2014★ 8 cited
Accessibility percolation with backsteps
Julien Berestycki, Éric Brunet, Zhan Shi
Consider a graph in which each site is endowed with a value called \emph{fitness}. A path in the graph is said to be "open" or "accessible" if the fitness values along that path is…
math.PR2013★ 34 cited
The number of accessible paths in the hypercube
Julien Berestycki, Éric Brunet, Zhan Shi
Motivated by an evolutionary biology question, we study the following problem: we consider the hypercube where each node carries an independent random variable uniforml…