Аннотация:
We consider a branching-selection particle system on the real line, introduced by Brunet and Derrida in [Phys. Rev. E, 56 (1997), pp. 2597–2604]. In this model the size of the population is fixed to a constant N. At each step individuals in the population reproduce independently, making children around their current position. Only the N rightmost children survive to reproduce at the next step. Bérard and Gouéré studied the speed at which the cloud of individuals drifts in [Comm. Math. Phys., 298 (2010), pp. 323–342], assuming the tails of the displacement decays at exponential rate; Bérard and Maillard [Electron. J. Probab., 19 (2014), 22] took interest in the case of heavy tail displacements. We take interest in an intermediate model, considering branching random walks in which the critical “spine” behaves as an α-stable random walk.
Ключевые слова:
branching random walk, selection, stable distribution.
Образец цитирования:
B. Mallein, “N-Branching random walk with α-stable spine”, Теория вероятн. и ее примен., 62:2 (2017), 365–392; Theory Probab. Appl., 62:2 (2018), 295–318
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\paper $N$-Branching random~walk with $\alpha$-stable spine
\jour Теория вероятн. и ее примен.
\yr 2017
\vol 62
\issue 2
\pages 365--392
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\jour Theory Probab. Appl.
\yr 2018
\vol 62
\issue 2
\pages 295--318
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tvp5117
https://doi.org/10.4213/tvp5117
https://www.mathnet.ru/rus/tvp/v62/i2/p365
Эта публикация цитируется в следующих 4 статьяx:
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, Sanjay Ramassamy, “Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models”, Probab. Surveys, 21:none (2024)
B. Mallein, S. Ramassamy, “Barak-erdos graphs and the infinite-bin model”, Ann. Inst. Henri Poincare-Probab. Stat., 57:4 (2021), 1940–1967
B. Mallein, “Necessary and sufficient conditions for the convergence of the consistent maximal displacement of the branching random walk”, Braz. J. Probab. Stat., 33:2 (2019), 356–373
Cortines A., Mallein B., “The Genealogy of An Exactly Solvable Ornstein-Uhlenbeck Type Branching Process With Selection”, Electron. Commun. Probab., 23 (2018), 98
Цитирование в формате AMSBIB
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