arXiv - MATH - Probability最新文献_第9页

Network evolution with Macroscopic Delays: asymptotics and condensation 具有宏观延迟的网络演化：渐进与凝聚

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.06048

Sayan Banerjee, Shankar Bhamidi, Partha Dey, Akshay Sakanaveeti

{"title":"Network evolution with Macroscopic Delays: asymptotics and condensation","authors":"Sayan Banerjee, Shankar Bhamidi, Partha Dey, Akshay Sakanaveeti","doi":"arxiv-2409.06048","DOIUrl":"https://doi.org/arxiv-2409.06048","url":null,"abstract":"Driven by the explosion of data and the impact of real-world networks, a wide\u0000array of mathematical models have been proposed to understand the structure and\u0000evolution of such systems, especially in the temporal context. Recent advances\u0000in areas such as distributed cyber-security and social networks have motivated\u0000the development of probabilistic models of evolution where individuals have\u0000only partial information on the state of the network when deciding on their\u0000actions. This paper aims to understand models incorporating emph{network\u0000delay}, where new individuals have information on a time-delayed snapshot of\u0000the system. We consider the setting where one has macroscopic delays, that is,\u0000the ``information'' available to new individuals is the structure of the\u0000network at a past time, which scales proportionally with the current time and\u0000vertices connect using standard preferential attachment type dynamics. We\u0000obtain the local weak limit for the network as its size grows and connect it to\u0000a novel continuous-time branching process where the associated point process of\u0000reproductions emph{has memory} of the entire past. A more tractable `dual\u0000description' of this branching process using an `edge copying mechanism' is\u0000used to obtain degree distribution asymptotics as well as necessary and\u0000sufficient conditions for condensation, where the mass of the degree\u0000distribution ``escapes to infinity''. We conclude by studying the impact of the\u0000delay distribution on macroscopic functionals such as the root degree.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212049","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: 0

Largest eigenvalue of positive mean Gaussian matrices 正均值高斯矩阵的最大特征值

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.05858

Arijit Chakrabarty, Rajat Subhra Hazra, Moumanti Podder

引用次数: 0

The nerd snipers problem 书呆子狙击手问题

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.06068

Boris Alexeev, Dustin Mixon

引用次数: 0

Thermalization And Convergence To Equilibrium Of The Noisy Voter Model 噪声选民模型的热化和趋于平衡

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.05722

Enzo Aljovin, Milton Jara, Yangrui Xiang

{"title":"Thermalization And Convergence To Equilibrium Of The Noisy Voter Model","authors":"Enzo Aljovin, Milton Jara, Yangrui Xiang","doi":"arxiv-2409.05722","DOIUrl":"https://doi.org/arxiv-2409.05722","url":null,"abstract":"We investigate the convergence towards equilibrium of the noisy voter model,\u0000evolving in the complete graph with n vertices. The noisy voter model is a\u0000version of the voter model, on which individuals change their opinions randomly\u0000due to external noise. Specifically, we determine the profile of convergence,\u0000in Kantorovich distance (also known as 1-Wasserstein distance), which\u0000corresponds to the Kantorovich distance between the marginals of a\u0000Wright-Fisher diffusion and its stationary measure. In particular, we\u0000demonstrate that the model does not exhibit cut-off under natural noise\u0000intensity conditions. In addition, we study the time the model needs to forget\u0000the initial location of particles, which we interpret as the Kantorovich\u0000distance between the laws of the model with particles in fixed initial\u0000positions and in positions chosen uniformly at random. We call this process\u0000thermalization and we show that thermalization does exhibit a cut-off profile.\u0000Our approach relies on Stein's method and analytical tools from PDE theory,\u0000which may be of independent interest for the quantitative study of observables\u0000of Markov chains.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212053","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: 0

Non-Equilibrium Fluctuations for a Spatial Logistic Branching Process with Weak Competition 弱竞争空间逻辑分支过程的非平衡波动

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.05269

Thomas Tendron

引用次数: 0

The emptiness formation probability, and representations for nonlocal correlation functions, of the 20-vertex model 20 个顶点模型的虚空形成概率和非局部相关函数表示法

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.05309

Pete Rigas

引用次数: 0

A refinement of the multinomial distribution with application 多项式分布的改进与应用

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.05788

Andrew V. Sills

引用次数: 0

A note on the fluctuations of the resolvent traces of a tensor model of sample covariance matrices 关于样本协方差矩阵张量模型解析痕量波动的说明

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.06007

Alicja Dembczak-Kołodziejczyk

引用次数: 0

Logarithmic delocalization of low temperature 3D Ising and Potts interfaces above a hard floor 硬地板上方低温三维伊辛和波茨界面的对数去焦化

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.06079

Joseph Chen, Reza Gheissari, Eyal Lubetzky

{"title":"Logarithmic delocalization of low temperature 3D Ising and Potts interfaces above a hard floor","authors":"Joseph Chen, Reza Gheissari, Eyal Lubetzky","doi":"arxiv-2409.06079","DOIUrl":"https://doi.org/arxiv-2409.06079","url":null,"abstract":"We study the entropic repulsion of the low temperature 3D Ising and Potts\u0000interface in an $ntimes n times n$ box with blue boundary conditions on its\u0000bottom face (the hard floor), and red boundary conditions on its other five\u0000faces. For Ising, Frohlich and Pfister proved in 1987 that the typical\u0000interface height above the origin diverges (non-quantitatively), via\u0000correlation inequalities special to the Ising model; no such result was known\u0000for Potts. We show for both the Ising and Potts models that the entropic\u0000repulsion fully overcomes the potentially attractive interaction with the\u0000floor, and obtain a logarithmically diverging lower bound on the typical\u0000interface height. This is complemented by a conjecturally sharp upper bound of\u0000$lfloor xi^{-1}log nrfloor$ where $xi$ is the rate function for a\u0000point-to-plane non-red connection under the infinite volume red measure. The\u0000proof goes through a coupled random-cluster interface to overcome the potential\u0000attractive interaction with the boundary, and a coupled fuzzy Potts model to\u0000reduce the upper bound to a simpler setting where the repulsion is attained by\u0000conditioning a no-floor interface to lie in the upper half-space.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"410 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212042","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: 0

Random Chowla's Conjecture for Rademacher Multiplicative Functions 拉德马赫乘法函数的随机乔拉猜想

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.05952

Jake Chinis, Besfort Shala

引用次数: 0