Random Structures & Algorithms最新文献_第2页

The upper tail problem for induced 4‐cycles in sparse random graphs 稀疏随机图中诱导4 -环的上尾问题

3区数学

Random Structures & Algorithms Pub Date : 2023-10-16 DOI: 10.1002/rsa.21187

Asaf Cohen Antonir

引用次数: 3

A down‐up chain with persistent labels on multifurcating trees 在多分形树上具有持久标签的自上而下链

3区数学

Random Structures & Algorithms Pub Date : 2023-10-12 DOI: 10.1002/rsa.21185

Frederik Sørensen

{"title":"A down‐up chain with persistent labels on multifurcating trees","authors":"Frederik Sørensen","doi":"10.1002/rsa.21185","DOIUrl":"https://doi.org/10.1002/rsa.21185","url":null,"abstract":"Abstract In this article, we propose to study a general notion of a down‐up Markov chain for multifurcating trees with labeled leaves. We study in detail down‐up chains associated with the ‐model of Chen et al. (Electron. J. Probab. 14 (2009), 400–430.), generalizing and further developing previous work by Forman et al. (arXiv:1802.00862, 2018; arXiv:1804.01205, 2018; arXiv:1809.07756, 2018; Random Struct. Algoritm. 54 (2020), 745–769; Electron. J. Probab. 25 (2020), 1–46.) in the binary special cases. The technique we deploy utilizes the construction of a growth process and a down‐up Markov chain on trees with planar structure. Our construction ensures that natural projections of the down‐up chain are Markov chains in their own right. We establish label dynamics that at the same time preserve the labeled alpha‐gamma distribution and keep the branch points between the smallest labels for order time steps for all . We conjecture the existence of diffusive scaling limits generalizing the “Aldous diffusion” by Forman et al. (arXiv:1802.00862, 2018; arXiv:1804.01205, 2018; arXiv:1809.07756, 2018.) as a continuum‐tree‐valued process and the “algebraic ‐Ford tree evolution” by Löhr et al. (Ann. Probab. 48 (2020), 2565–2590.) and by Nussbaumer and Winter (arXiv:2006.09316, 2020.) as a process in a space of algebraic trees.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135923549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

A full characterization of invariant embeddability of unimodular planar graphs 单模平面图不变嵌入性的完整刻画

3区数学

Random Structures & Algorithms Pub Date : 2023-10-04 DOI: 10.1002/rsa.21188

Ádám Timár, László Márton Tóth

引用次数: 2

Extremal results on feedback arc sets in digraphs 有向图中反馈弧集的极值结果

IF 1 3区数学

Random Structures & Algorithms Pub Date : 2023-08-21 DOI: 10.1002/rsa.21179

J. Fox, Z. Himwich, Nitya Mani

引用次数: 0

The birth of the strong components 诞生了强大的组件

IF 1 3区数学

Random Structures & Algorithms Pub Date : 2023-08-07 DOI: 10.1002/rsa.21176

S. Dovgal, Élie de Panafieu, D. Ralaivaosaona, Vonjy Rasendrahasina, S. Wagner

{"title":"The birth of the strong components","authors":"S. Dovgal, Élie de Panafieu, D. Ralaivaosaona, Vonjy Rasendrahasina, S. Wagner","doi":"10.1002/rsa.21176","DOIUrl":"https://doi.org/10.1002/rsa.21176","url":null,"abstract":"It is known that random directed graphs undergo a phase transition around the point . Earlier, Łuczak and Seierstad have established that as when , the asymptotic probability that the strongly connected components of a random directed graph are only cycles and single vertices decreases from 1 to 0 as goes from to . By using techniques from analytic combinatorics, we establish the exact limiting value of this probability as a function of and provide more statistical insights into the structure of a random digraph around, below and above its transition point. We obtain the limiting probability that a random digraph is acyclic and the probability that it has one strongly connected complex component with a given difference between the number of edges and vertices (called excess). Our result can be extended to the case of several complex components with given excesses as well in the whole range of sparse digraphs. Our study is based on a general symbolic method which can deal with a great variety of possible digraph families, and a version of the saddle point method which can be systematically applied to the complex contour integrals appearing from the symbolic method. While the technically easiest model is the model of random multidigraphs, in which multiple edges are allowed, and where edge multiplicities are sampled independently according to a Poisson distribution with a fixed parameter , we also show how to systematically approach the family of simple digraphs, where multiple edges are forbidden, and where 2‐cycles are either allowed or not. Our theoretical predictions are supported by numerical simulations when the number of vertices is finite, and we provide tables of numerical values for the integrals of Airy functions that appear in this study.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"36 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89550802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Threshold for detecting high dimensional geometry in anisotropic random geometric graphs 在各向异性随机几何图中检测高维几何的阈值

3区数学

Random Structures & Algorithms Pub Date : 2023-08-01 DOI: 10.1002/rsa.21178

Matthew Brennan, Guy Bresler, Brice Huang

引用次数: 1

The impact of heterogeneity and geometry on the proof complexity of random satisfiability 异质性和几何对随机可满足性证明复杂性的影响

3区数学

Random Structures & Algorithms Pub Date : 2023-06-28 DOI: 10.1002/rsa.21168

Thomas Bläsius, Tobias Friedrich, Andreas Göbel, Jordi Levy, Ralf Rothenberger

引用次数: 1

Universality of superconcentration in the Sherrington–Kirkpatrick model 谢林顿-柯克帕特里克模型中超集中的普遍性

IF 1 3区数学

Random Structures & Algorithms Pub Date : 2023-02-08 DOI: 10.1002/rsa.21183

Wei-Kuo Chen, Wai-Kit Lam

引用次数: 0

Optimal bisections of directed graphs 有向图的最优等分

IF 1 3区数学

Random Structures & Algorithms Pub Date : 2023-02-08 DOI: 10.1002/rsa.21175

Guanwu Liu, Jie Ma, C. Zu

引用次数: 0

On the largest part size of low‐rank combinatorial assemblies 关于低阶组合装配的最大零件尺寸

IF 1 3区数学

Random Structures & Algorithms Pub Date : 2022-12-30 DOI: 10.1002/rsa.21132

R. Arratia, S. Desalvo

{"title":"On the largest part size of low‐rank combinatorial assemblies","authors":"R. Arratia, S. Desalvo","doi":"10.1002/rsa.21132","DOIUrl":"https://doi.org/10.1002/rsa.21132","url":null,"abstract":"We give a general framework for approximations to decomposable combinatorial structures suitable to the situation where the size n$$ n $$ and the number of components k$$ k $$ are specified. In particular for assemblies, this involves a Poisson process, which, with the appropriate choice of parameter, may be viewed as an extension of saddlepoint approximation. We illustrate the use of the Poisson process description for assemblies by analyzing the component structure when the rank, defined as r:=n−k$$ r:= n-k $$ , is small relative to the size n$$ n $$ . There is near‐universal behavior, in the sense that, apart from degenerate cases where the exponential generating function has radius of convergence zero, we have for t∈(0,∞)$$ tin left(0,infty right) $$ and ℓ=1,2,…$$ ell =1,2,dots $$ : when r≍nα$$ rasymp {n}^{alpha } $$ for fixed α∈(ℓℓ+1,ℓ+1ℓ+2)$$ alpha in left(frac{ell }{ell +1},frac{ell +1}{ell +2}right) $$ , the size L1$$ {L}_1 $$ of the largest component converges in probability to ℓ+2$$ ell +2 $$ ; when r∼tnℓ/(ℓ+1)$$ rsim tkern0.3em {n}^{ell /left(ell +1right)} $$ , we have ℙ(L1∈{ℓ+1,ℓ+2})→1$$ mathbb{P}left({L}_1in left{ell +1,ell +2right}right)to 1 $$ , with the choice governed by a Poisson limit distribution for the number of components of size ℓ+2$$ ell +2 $$ . This was recently observed, for the case ℓ=1$$ ell =1 $$ and the special cases of permutations and set partitions, using Chen–Stein approximations for the indicators of attacks and alignments in rook placements.","PeriodicalId":54523,"journal":{"name":"Random Structures & Algorithms","volume":"145 14 1","pages":"26 - 3"},"PeriodicalIF":1.0,"publicationDate":"2022-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80219358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1