Genealogies of Interacting Particle Systems最新文献

FRONT MATTER 前页

Genealogies of Interacting Particle Systems Pub Date : 2020-02-24 DOI: 10.1142/9789811206092_fmatter

M. Birkner, Rongfeng Sun, J. Swart

引用次数: 0

Markovian Dynamics of Exchangeable Arrays 可交换阵列的马尔可夫动力学

Genealogies of Interacting Particle Systems Pub Date : 2018-10-31 DOI: 10.1142/9789811206092_0005

J. vCern'y, A. Klimovsky

引用次数: 3

On Projections of the Supercritical Contact Process: Uniform Mixing and Cutoff Phenomenon 超临界接触过程的投影:均匀混合和切断现象

Genealogies of Interacting Particle Systems Pub Date : 2018-10-16 DOI: 10.1142/9789811206092_0009

Stein Andreas Bethuelsen

引用次数: 1

Stochastic Evolution of Genealogies of Spatial Populations: State Description, Characterization of Dynamics and Properties 空间种群谱系的随机演化:状态描述、动态特征和特性

Genealogies of Interacting Particle Systems Pub Date : 2018-07-10 DOI: 10.1142/9789811206092_0002

A. Depperschmidt, A. Greven

引用次数: 4

PATRICIA Bridges 帕特丽夏的桥梁

Genealogies of Interacting Particle Systems Pub Date : 2018-06-16 DOI: 10.1142/9789811206092_0006

Steven N. Evans, A. Wakolbinger

{"title":"PATRICIA Bridges","authors":"Steven N. Evans, A. Wakolbinger","doi":"10.1142/9789811206092_0006","DOIUrl":"https://doi.org/10.1142/9789811206092_0006","url":null,"abstract":"A radix sort tree arises when storing distinct infinite binary words in the leaves of a binary tree such that for any two words their common prefixes coincide with the common prefixes of the corresponding two leaves. If one deletes the out-degree $1$ vertices in the radix sort tree and \"closes up the gaps\", then the resulting PATRICIA tree maintains all the information that is necessary for sorting the infinite words into lexicographic order. We investigate the PATRICIA chains -- the tree-valued Markov chains that arise when successively building the PATRICIA trees for the collection of infinite binary words $Z_1,ldots, Z_n$, $n=1,2,ldots$, where the source words $Z_1, Z_2,ldots$ are independent and have a common diffuse distribution on ${0,1}^infty$. It turns out that the PATRICIA chains share a common collection of backward transition probabilities and that these are the same as those of a chain introduced by R'emy for successively generating uniform random binary trees with larger and larger numbers of leaves. This means that the infinite bridges of any PATRICIA chain (that is, the chains obtained by conditioning a PATRICIA chain on its remote future) coincide with the infinite bridges of the R'emy chain. The infinite bridges of the R'emy chain are characterized concretely in Evans, Gr\"ubel, and Wakolbinger 2017 and we recall that characterization here while adding some details and clarifications.","PeriodicalId":163241,"journal":{"name":"Genealogies of Interacting Particle Systems","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126708115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Coexistence and Duality in Competing Species Models 竞争物种模型中的共存与二元性

Genealogies of Interacting Particle Systems Pub Date : 2018-02-28 DOI: 10.1142/9789811206092_0001

Yu-Ting Chen, Matthias Hammer

引用次数: 0

The Algebraic Approach to Duality: An Introduction 对偶的代数方法:导论

Genealogies of Interacting Particle Systems Pub Date : 2018-02-20 DOI: 10.1142/9789811206092_0003

A. Sturm, J. Swart, F. Vollering

引用次数: 11

Collision Times of Random Walks and Applications to the Brownian Web 随机漫步的碰撞时间及其在布朗网中的应用

Genealogies of Interacting Particle Systems Pub Date : 2015-08-27 DOI: 10.1142/9789811206092_0007

D. Coupier, K. Saha, A. Sarkar, V. Tran

{"title":"Collision Times of Random Walks and Applications to the Brownian Web","authors":"D. Coupier, K. Saha, A. Sarkar, V. Tran","doi":"10.1142/9789811206092_0007","DOIUrl":"https://doi.org/10.1142/9789811206092_0007","url":null,"abstract":"Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Fontes Isopi Newman and Ravishankar (2004). One of their convergence condition, called (B2), roughly states that the probability that the first collision time of three paths, crossing a small segment of length $varepsilon$, bigger than $t (>0)$ is of small order of $varepsilon$, i.e., $o(varepsilon)$. Condition (B2) is often verified by applying an FKG type correlation inequality together with a coalescing time tail estimate for two paths. For many models where paths have complex interactions, it is hard to establish FKG type inequalities. In this paper, we show that for a non-crossing path model, with some homogeneity and Markovian properties, a suitable upper bound on expected first collision time for three paths can be obtained directly using Lyapunov functions and that provides an alternate verification of Condition (B2). We further show that in case of independent simple symmetric one dimensional random walks or in case of independent Brownian motions the expected value can be computed explicitly. \u0000We apply this alternate method of verification of (B2) to several models in the basin of attraction of the Brownian web studied earlier in the literature.","PeriodicalId":163241,"journal":{"name":"Genealogies of Interacting Particle Systems","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116888171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1