2024
DOI: 10.1051/ps/2024014
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Branching random walks with regularly varying perturbations

Krzysztof Kowalski

Abstract: We consider a modification of classical branching random walk, where we add i.i.d. perturbations to the positions of the particles in each generation. In this model, which was introduced and studied by Bandyopadhyay and Ghosh (2023), perturbations take the form 1/θ log X/E where θ is a positive parameter, X has an arbitrary distribution μ and E is exponential with parameter 1, independent of X. Working under finite mean assumption for μ, they proved almost sure convergence of the rightmost position to a consta… Show more

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