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Maxima of branching random walks vs. independent random walks

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  • Durrett, Richard

Abstract

In recent years several authors have obtained limit theorems for the location of the right most particle in a supercritical branching random walk. In this paper we will consider analogous problems for an exponentially growing number of independent random walks. A comparison of our results with the known results of branching random walk then identifies the limit behaviors which are due to the number of particles and those which are determined by the branching structure.

Suggested Citation

  • Durrett, Richard, 1979. "Maxima of branching random walks vs. independent random walks," Stochastic Processes and their Applications, Elsevier, vol. 9(2), pages 117-135, November.
    • Handle: RePEc:eee:spapps:v:9:y:1979:i:2:p:117-135
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    Citations

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    Cited by:

    1. Zakhar Kabluchko, 2012. "Limit Laws for Sums of Independent Random Products: the Lattice Case," Journal of Theoretical Probability, Springer, vol. 25(2), pages 424-437, June.
    2. Bhattacharya, Ayan & Hazra, Rajat Subhra & Roy, Parthanil, 2018. "Branching random walks, stable point processes and regular variation," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 182-210.
    3. Viktor Bezborodov & Luca Persio & Tyll Krueger, 2021. "A Shape Theorem for a One-Dimensional Growing Particle System with a Bounded Number of Occupants per Site," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2265-2284, December.
    4. Engelke, Sebastian & Kabluchko, Zakhar, 2015. "Max-stable processes and stationary systems of Lévy particles," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4272-4299.
    5. Ray, Souvik & Hazra, Rajat Subhra & Roy, Parthanil & Soulier, Philippe, 2023. "Branching random walk with infinite progeny mean: A tale of two tails," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 120-160.

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