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Ordering of Random Walks: The Leader and the Laggard
D. ben-Avraham, B. M. Johnson, C. A. Monaco +2
We investigate two complementary problems related to maintaining the relative positions of N random walks on the line: (i) the leader problem, that is, the probability {\cal L}_N(t…
Compact directed percolation with movable partial reflectors
Ronald Dickman, Daniel ben-Avraham
We study a version of compact directed percolation (CDP) in one dimension in which occupation of a site for the first time requires that a "mine" or antiparticle be eliminated. Thi…
Efficient Immunization Strategies for Computer Networks and Populations
Reuven Cohen, Shlomo Havlin, Daniel ben-Avraham
We present an effective immunization strategy for computer networks and populations with broad and, in particular, scale-free degree distributions. The proposed strategy, acquainta…
Asymptotic analysis of a random walk with a history-dependent step length
Ronald Dickman, Francisco Fontenele Araujo, Daniel ben-Avraham
We study an unbiased, discrete time random walk on the nonnegative integers, with the origin absorbing. The process has a history-dependent step length: the walker takes steps of l…
Scale-free Networks on Lattices
Alejandro F. Rozenfeld, Reuven Cohen, Daniel ben-Avraham +1
We suggest a method for embedding scale-free networks, with degree distribution P(k) k^-lambda, in regular Euclidean lattices. The embedding is driven by a natural constraint of mi…
Percolation in Directed Scale-Free Networks
N. Schwartz, R. Cohen, D. ben-Avraham +2
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such d…