Abstract
The paper completes the investigation of limit distribution of the number of particles at the source of branching in the model of critical catalytic branching random walk on \( {{\mathbb Z}^d}\;d \in {\mathbb N} \). Limit theorems of such kind were established only for d = 1, 2, 3, 4 under the assumption that, at the initial moment, there is a single particle at the source of branching. We prove their analog for \( d \geqslant 5 \). Moreover, in any dimension, we generalize the previous results by permitting the initial particle to start at an arbitrary point of the lattice.
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The work is partially supported by the RFBR grant 10-01-00266.
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Bulinskaya, E.V. Limit distributions arising in branching random walks on integer lattices. Lith Math J 51, 310–321 (2011). https://doi.org/10.1007/s10986-011-9128-2
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DOI: https://doi.org/10.1007/s10986-011-9128-2