Events and their probabilities random variables and their distributions discrete random variables continuous random variables generating functions and their applications Markov chains convergence of… Expand

We consider the problem of finding the shortest distance between all pairs of vertices in a complete digraph on n vertices, whose arc-lengths are non-negative random variables.Expand

The influence theorem for product measures on the discrete space (0, 1} N may be extended to probability measures with the property of monotonicity (which is equivalent to "strong positive… Expand

We consider the task of detecting a salient cluster in a sensor network, that is, an undirected graph with a random variable attached to each node. Motivated by recent research in environmental… Expand

We prove that the critical value βc of a ferromagnetic Potts model is astrictly decreasing function of the strengths of interaction of the process. This is achieved in the (more) general context of… Expand

We prove a locality theorem for connective constants, namely, that the connective constant of two graphs are close in value whenever the graphs agree on a large ball around the origin (and a further condition is satisfied).Expand

We study the asymptotic scaling of the entanglement of a block of spins for the ground state of the one-dimensional quantum Ising model with transverse field. When the field is sufficiently strong,… Expand

We prove the existence of a (random) Lipschitz function F : Z → Z such that, for every x ∈ Z, the site (x, F (x)) is open in a site percolation process on Z. The Lipschitz constant may be taken to be… Expand