Let W 1 ... . , W N be N nonnegative random variables and let 9J~ be the class of all probability measures on [0, m). Define a transformation T on 9J~ by letting T# be the distribution of W a X 1 + .â€¦ (More)

We introduce the class of strongly Rayleigh probability measures by means of geometric properties of their generating polynomials that amount to the stability of the latter. This class contains e.g.â€¦ (More)

Consider the infinite particle system on the integers with the simple exclusion interaction and one-particle motion determined by p{x, x + 1) = p and p(x, x 1) = q for x e Z, where p + q = 1 and p >â€¦ (More)

We prove for the contact process on Z, and many other graphs, that the upper invariant measure dominates a homogeneous product measure with large density if the infection rate Î» is sufficientlyâ€¦ (More)

where Î·x,y is the configuration obtained from Î· by interchanging the coordinates Î·(x) and Î·(y). Here p(x, y) = p(y, x) are the transition probabilities for a symmetric, irreducible, Markov chain onâ€¦ (More)

We propose the following simple stochastic model for phylogenetic trees. New types are born and die according to a birth and death chain. At each birth we associate a fitness to the new type sampledâ€¦ (More)