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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2022, Volume 316, Pages 32–46
DOI: https://doi.org/10.4213/tm4217
(Mi tm4217)
 

This article is cited in 3 scientific papers (total in 3 papers)

Capacity of the Range of Branching Random Walks in Low Dimensions

Tianyi Bai, Yueyun Hu

LAGA, Université Sorbonne Paris Nord, 99 avenue J.-B. Clément, F-93430 Villetaneuse, France
Full-text PDF (281 kB) Citations (3)
References:
Abstract: Consider a branching random walk $(V_u)_{u\in \mathcal T^{\mathrm{IGW}}}$ in $\mathbb Z^d$ with the genealogy tree $\mathcal T^{\mathrm{IGW}}$ formed by a sequence of i.i.d. critical Galton–Watson trees. Let $R_n$ be the set of points in $\mathbb Z^d$ visited by $(V_u)$ when the index $u$ explores the first $n$ subtrees in $\mathcal T^{\mathrm{IGW}}$. Our main result states that for $d\in \{3,4,5\}$, the capacity of $R_n$ is almost surely equal to $n^{(d-2)/{2}+o(1)}$ as $n\to \infty $.
Keywords: branching random walk, tree-indexed random walk, capacity.
Received: April 22, 2021
Revised: July 8, 2021
Accepted: October 13, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2022, Volume 316, Pages 26–39
DOI: https://doi.org/10.1134/S0081543822010047
Bibliographic databases:
Document Type: Article
UDC: 519.218.2
MSC: 60J80, 60J65
Language: Russian
Citation: Tianyi Bai, Yueyun Hu, “Capacity of the Range of Branching Random Walks in Low Dimensions”, Branching Processes and Related Topics, Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin, Trudy Mat. Inst. Steklova, 316, Steklov Math. Inst., Moscow, 2022, 32–46; Proc. Steklov Inst. Math., 316 (2022), 26–39
Citation in format AMSBIB
\Bibitem{BaiHu22}
\by Tianyi~Bai, Yueyun~Hu
\paper Capacity of the Range of Branching Random Walks in Low Dimensions
\inbook Branching Processes and Related Topics
\bookinfo Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 316
\pages 32--46
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4217}
\crossref{https://doi.org/10.4213/tm4217}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 316
\pages 26--39
\crossref{https://doi.org/10.1134/S0081543822010047}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140789904}
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  • https://doi.org/10.4213/tm4217
  • https://www.mathnet.ru/eng/tm/v316/p32
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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