We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed vP . We give upper bounds on the quenched probability that at least one of the random walks started in the interval [An, Bn] has traveled a distance of less than (vP − ε)n. This leads to both a uniform law of large numbers an...

The random assignment problem is to minimize the cost of an assignment in a n×n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2, . . . , m, for m = n or n, and random permutations of 1, 2, . . . , n for each row, or of 1, 2, . . . , n for the whole matrix. We find the limit of the expected cos...

This is a survey of the main methods in non-uniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, a...

In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (δ, s, n)-nets of low discrepancy. It turns out that optimum distributions have a rich combinatorial structure. Namely, we show that optimum distributions can be characterized completely as maximum dis...

Nestedness has received considerable attention in community ecology and conservation biology from both theoretical and empirical perspectives. This has lead to the creation of various metrics and null models to analyze nested subsets, all of which rely on the random placement of species to assess significance. However, if immigration and extinction are the processes that underlie species distri...

Random Boolean networks (RBNs) were first introduced and used to model regulatory gene networks by Kauffman in 1969 and since then have been frequently used to model networks at various levels of biological organization. The standard model has a characteristic topology in which the network has N genes with an average of K input connections selected at random. We have used RBNs to examine regula...