Abstract
We consider a supercritical continuous-time branching random walk on a multidimensional lattice with finite number of particle generation sources of the same intensities without any restrictions on the variance of jumps of the underlying random walk. The effect of “limit coalescence” of eigenvalues is revealed for an arrangement of sources under which the pairwise distances between them go off to infinity. The effect of the arrangement of particle generation sources on the order of appearance of positive eigenvalues in the spectrum of the evolutionary operator with receding sources is revealed.
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Notes
- 1.
The condition of linear independence of the vectors u and v can be replaced by the condition that the quantities l (k) grow faster than k, for example, l (k) ≥ k 2. In this case, the sequence of configurations {S (k)} is also receding.
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This work was supported by the Russian Science Foundation under grant no. 19-11-00290 and was performed at the Steklov Mathematical Institute of Russian Academy of Sciences.
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Yarovaya, E.B. (2021). Influence of the Configuration of Particle Generation Sources on the Behavior of Branching Walks: A Case Study. In: Karapetyants, A.N., Pavlov, I.V., Shiryaev, A.N. (eds) Operator Theory and Harmonic Analysis. OTHA 2020. Springer Proceedings in Mathematics & Statistics, vol 358. Springer, Cham. https://doi.org/10.1007/978-3-030-76829-4_21
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