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Title: Branching random walks in non homogeneous environments Authors:  Elena Yarovaya - Lomonosov Moscow State University (Russia) [presenting]
Abstract: Nowadays it is commonly accepted that branching random walks are crucially useful in investigations of stochastic systems with birth, death and migration of their elements. The principal attention will be paid to the properties of branching random walks on multidimensional lattices. We will be mainly interested in the problems related to the limiting behavior of branching random walks such as existence of phase transitions under change of various parameters, the properties of the limiting distribution of the particle population, existence and the shape of the propagating fronts of particles, etc. The answer to these and other questions heavily depend on numerous factors which affect the properties of a branching random walk. Therefore, we will try to describe, how the properties of a branching walk depend on the fact of non homogeneity of the branching media, on the number and mutual disposition of the branching sources, and also on such properties of a branching walk as its symmetry and finiteness or infiniteness of the variance of jumps. We present also some results of simulation of branching random walks and discuss how they may be applied to numerical estimation of various characteristics describing the properties of the phase transitions.