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Asymptotics of branching symmetric random walk on the lattice with a single source. (English. Abridged French version) Zbl 0917.60080

The paper investigates the asymptotic behavior of a continuous-time branching random walk on \(Z^d\), \(d\geq 1\), in which particles may produce children only at a fixed point (source) of the lattice. Assuming that the random walk is homogeneous, irreducible and with jumps having zero mean and finite variance, the authors find the limiting extinction probability of the branching random walk initiated at time \(t=0\) by one particle and study the asymptotic behavior of integer moments for the total population size and the number of particles at a given site.

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G50 Sums of independent random variables; random walks
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