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A $N$-branching random walk with random selection [PDF]
Latin American Journal of Probability and Mathematical Statistics, 2016 We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its offspring are
Cortines, Aser, Mallein, Bastien
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Minima in branching random walks
The Annals of Probability, 2009 Given a branching random walk, let $M_n$ be the minimum position of any member of the $n$th generation. We calculate $\mathbf{E}M_n$ to within O(1) and prove exponential tail bounds for $\mathbf{P}\{|M_n-\mathbf{E}M_n|>x\}$, under quite general ...
Addario-Berry, Louigi, Reed, Bruce
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Random walk on barely supercritical branching random walk [PDF]
Probability Theory and Related Fields, 2019 Let $\mathcal{T}$ be a supercritical Galton-Watson tree with a bounded offspring distribution that has mean $ >1$, conditioned to survive. Let $ _{\mathcal{T}}$ be a random embedding of $\mathcal{T}$ into $\mathbb{Z}^d$ according to a simple random walk step distribution.
Remco van der Hofstad +2 more
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Theory of Branching and Annihilating Random Walks [PDF]
Physical Review Letters, 1996 4 pages, revtex, no figures; final version with slight changes, now accepted for publication in Phys.
John Cardy, Uwe C. Täuber
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Coalescing-Branching Random Walks on Graphs [PDF]
ACM Transactions on Parallel Computing, 2015 We study a distributed randomized information propagation mechanism in networks we call the coalescing-branching random walk (cobra walk, for short). A cobra walk is a generalization of the well-studied “standard” random walk, and is useful in modeling and understanding the Susceptible-Infected- Susceptible (SIS ...
Chinmoy Dutta +3 more
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Asymptotic behavior of survival probability for a branching random walk with a barrier
AIMS Mathematics, 2023 Consider a branching random walk with a mechanism of elimination. We assume that the underlying Galton-Watson process is supercritical, thus the branching random walk has a positive survival probability.
You Lv
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Branching Random Walks with Two Types of Particles on Multidimensional Lattices
Mathematics, 2022 We consider a continuous-time branching random walk on a multidimensional lattice with two types of particles and an infinite number of initial particles.
Iuliia Makarova +3 more
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Note on the Generalized Branching Random Walk on the Galton–Watson Tree
Fractal and Fractional, 2023 Let ∂T be a super-critical Galton–Watson tree. Recently, the first author computed almost surely and simultaneously the Hausdorff dimensions of the sets of infinite branches of the boundary of ∂T along which the sequence SnX(t)/SnX˜(t) has a given set of
Najmeddine Attia, Rim Amami, Rimah Amami
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Individuals at the origin in the critical catalytic branching random walk [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 A continuous time branching random walk on the lattice $\mathbb{Z}$ is considered in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we prove ...
Valentin Topchii, Vladimir Vatutin
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Inflationary theory of branching morphogenesis in the mouse salivary gland
Nature Communications, 2023 The mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing ...
Ignacio Bordeu +2 more
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