The monotonicity of the probability of return into the source in models of branching random walks |
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Authors: | E B Yarovaya |
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Institution: | (1) Department of Mathematics, Iowa State University, Ames, IA 50011, USA;(2) Indian Institute of Science, Bangalore, 560012, India |
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Abstract: | The paper discusses two models of a branching random walk on a many-dimensional lattice with birth and death of particles
at a single node being the source of branching. The random walk in the first model is assumed to be symmetric. In the second
model an additional parameter is introduced which enables “artificial” intensification of the prevalence of branching or walk
at the source and, as the result, violating the symmetry of the random walk. The monotonicity of the return probability into
the source is proved for the second model, which is a key property in the analysis of branching random walks. |
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