The Erlang weighted tree, a new branching process

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2023-10-23 DOI:10.1002/rsa.21180

Mehrdad Moharrami, Vijay Subramanian, Mingyan Liu, Rajesh Sundaresan

引用次数: 1

Abstract

Abstract In this paper, we study a new discrete tree and the resulting branching process, which we call the erlang weighted tree(EWT). The EWT appears as the local weak limit of a random graph model proposed in La and Kabkab, Internet Math. 11 (2015), no. 6, 528–554. In contrast to the local weak limit of well‐known random graph models, the EWT has an interdependent structure. In particular, its vertices encode a multi‐type branching process with uncountably many types. We derive the main properties of the EWT, such as the probability of extinction, growth rate, and so forth. We show that the probability of extinction is the smallest fixed point of an operator. We then take a point process perspective and analyze the growth rate operator. We derive the Krein–Rutman eigenvalue and the corresponding eigenfunctions of the growth operator, and show that the probability of extinction equals one if and only if .

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Erlang加权树，一个新的分支过程

本文研究了一种新的离散树及其分支过程，我们称之为厄朗加权树(EWT)。EWT作为La and Kabkab提出的随机图模型的局部弱极限出现，互联网数学，11 (2015)，no。6, 528 - 554。与众所周知的随机图模型的局部弱极限相比，EWT具有相互依赖的结构。特别是，它的顶点编码了一个具有不可数多类型的多类型分支过程。我们推导了EWT的主要性质，如灭绝概率、增长率等。我们证明了消光概率是算子的最小不动点。然后，我们从点过程的角度分析增长率算子。导出了生长算子的Krein-Rutman特征值和相应的特征函数，并证明了消光的概率等于1当且仅当。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.