![]() Next, the parent-child directions of the edges are. This is joint work with Marcel Ortgiese (University of Bath). A GaltonWatson tree is generated with a known offspring distribution, conditioned on its having n nodes. ![]() In particular, we can see that we need to consider the combined effect of fitness and offspring distribution to decide which scenario occurs. In this spirit, we give sufficient conditions on the fitness and offspring distribution for the contact process with fitness on Galton-Watson trees that either guarantee that there is a phase transition or that the process is always supercritical. Consider the -biased random walk fXngn 0 on T this is the nearest neighbor random walk which, when at a vertex v with dv o spring. We assume that the underlying population structure is given by a Galton-Watson tree. Recent works by Huang/Durrett and Bhamidi et al have given necessary and sufficient conditions on the offspring distribution for the classic contact process to exhibit a phase transition. The family tree of a supercritical Galton-Watson branching process with a single progenitor is called a Galton-Watson tree (a formal de nition is given later in this section). Informally, the associated cut-tree represents the genealogy of the nested connected components created by this process. random walks on Galton-Watson trees Yuval Peres Ofer Zeitouniy JAbstract Let T be a rooted Galton-Watson tree with o spring distribution fpkg that has p0 0, mean m P kpk > 1 and exponential tails. We consider a variant of the contact process, where vertices are equipped with a random fitness representing inhomogeneities among individuals. In this inhomogeneous contact process, the infection is passed along an edge with rate proportional to the product of the fitness values of the vertices on either end. offspring distribution) on the limit in distribution of a Galton-Watson tree conditioned on having a large number of individuals with out-degree in a given. as it is conducted according to the latest Watson is. Abstract: The contact process is a simple model for the spread of an infection in a structured population. Galton-Watson tree, Parametric estimation, Harris path, Brownian excursion, Real tree data, XML files, Wikipedia. programme He was one of the men of whom Galton And, when Bishop Watson.
0 Comments
Leave a Reply. |