Properties of critical branching random walks on the line under non-extinction condition | Sciact - Система учета научной деятельности ИМ СО РАН

Properties of critical branching random walks on the line under non-extinction condition Научная публикация

Журнал

Discrete Mathematics and Applications
ISSN: 0924-9265 , E-ISSN: 1569-3929

Вых. Данные

Год: 2025, Том: 35, Номер: 3, Страницы: 187-202 Страниц : 16 DOI: 10.1515/dma-2025-0014

Ключевые слова

branching random walk on a real line; Galton–Watson branching process; point process on a line; critical branching process; limit theorems; reduced genealogical trees

Авторы

Topchii Valentin A. ¹

Организации

1	Sobolev Institute of Mathematics SB RAS (Omsk division) , Novosibirsk Russia

Информация о финансировании (1)

Омский филиал ФГБУН «Институт математики им. С.Л. Соболева СО РАН».

FWNF-2022-0003

We study a critical branching random walk on a real line with discrete time controlled by a point process. Sizes of sequential generations form Galton–Watson critical process with one type of particles. The particle coordinates are interpreted as the weights of the vertices on the genealogical tree of the random walk. A reduced tree is obtained after removing branches of the genealogical tree that do not reach the n-th level. The asymptotic behavior of the first two moments of the number of vertices and of the sum of vertex weights over all levels of reduced tree under condition of nonextinction is described. Several limit theorems for the weights of particles in a branching random walk up to n-th generation under condition of nonextinction are proved.

Topchii V.A.
Properties of critical branching random walks on the line under non-extinction condition
Discrete Mathematics and Applications. 2025. V.35. N3. P.187-202. DOI: 10.1515/dma-2025-0014 WOS Scopus OpenAlex

Топчий В.А.
Свойства критических ветвящихся случайных блужданий на прямой при условии невырождения
Дискретная математика. 2023. Т.35. №1. С.107-127. DOI: 10.4213/dm1709 РИНЦ OpenAlex

Поступила в редакцию:	18 апр. 2022 г.
Принята к публикации:	29 окт. 2022 г.
Опубликована в печати:	26 июн. 2025 г.
Опубликована online:	25 июл. 2025 г.

Web of science:	WOS:001529353200003
Scopus:	2-s2.0-105011083143
OpenAlex:	W4412433076

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