We study the problem of coexistence in a two-type competition model governed by first-passage percolation on Zd or on the infinite cluster in Bernoulli percolation. We prove for a large class ofâ€¦ (More)

The aim of this paper is to extend the well-known asymptotic shape result for first-passage percolation on Z to first-passage percolation on a random environment given by the infinite cluster of aâ€¦ (More)

The asymptotic shape theorem for the contact process in random environment gives the existence of a norm Î¼ on R such that the hitting time t(x) is asymptotically equivalent to Î¼(x) when the contactâ€¦ (More)

The chemical distance D(x, y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behaviour of thisâ€¦ (More)

We prove the continuity of the shape governing the asymptotic growth of the supercritical contact process in Z, with respect to the infection parameter. The proof is valid in any dimension d â‰¥ 1.

By simulating the observations of multiple satellite instruments, COSP enables quantitative evaluation of clouds, humidity, and precipitation processes in diverse numerical models. G eneralâ€¦ (More)

It has long been known that antibiotic treatment will not completely kill off a bacteria population. For many species a small fraction of bacteria is not sensitive to antibiotics. These bacteria areâ€¦ (More)

The advice contained in this document should be read in conjunction with relevant federal, provincial, territorial and local legislation, regulations, and policies. Recommended measures should not beâ€¦ (More)

Consider two epidemics whose expansions on Z are governed by two families of passage times that are distinct and stochastically comparable. We prove that when the weak infection survives, the spaceâ€¦ (More)