arXiv - MATH - Probability最新文献_第10页

Trend to equilibrium and Newtonian limit for the relativistic Langevin equation with singular potentials 具有奇异势能的相对论性朗格文方程的平衡趋势和牛顿极限

arXiv - MATH - Probability Pub Date : 2024-09-09 DOI: arxiv-2409.05645

Manh Hong Duong, Hung Dang Nguyen

引用次数: 0

Asymmetric exclusion process with long-range interactions 具有长程相互作用的不对称排斥过程

arXiv - MATH - Probability Pub Date : 2024-09-08 DOI: arxiv-2409.05017

V. Belitsky, N. P. N. Ngoc, G. M. Schütz

{"title":"Asymmetric exclusion process with long-range interactions","authors":"V. Belitsky, N. P. N. Ngoc, G. M. Schütz","doi":"arxiv-2409.05017","DOIUrl":"https://doi.org/arxiv-2409.05017","url":null,"abstract":"We consider asymmetric simple exclusion processes with $N$ particles on the\u0000one-dimensional discrete torus with $L$ sites with following properties: (i)\u0000nearest-neighbor jumps on the torus, (ii) the jump rates depend only on the\u0000distance to the next particle in the direction of the jump, (iii) the jump\u0000rates are independent of $N$ and $L$. For measures with a long-range two-body\u0000interaction potential that depends only on the distance between neighboring\u0000particles we prove a relation between the interaction potential and particle\u0000jump rates that is necessary and sufficient for the measure to be invariant for\u0000the process. The normalization of the measure and the stationary current are\u0000computed both for finite $L$ and $N$ and in the thermodynamic limit. For a\u0000finitely many particles that evolve on $mathbb{Z}$ with totally asymmetric\u0000jumps it is proved, using reverse duality, that a certain family of\u0000nonstationary measures with a microscopic shock and antishock evolves into a\u0000convex combination of such measures with weights given by random walk\u0000transition probabilities. On macroscopic scale this domain random walk is a\u0000travelling wave phenomenon tantamount to phase separation with a stable shock\u0000and stable antishock. Various potential applications of this result and open\u0000questions are outlined.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212152","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

Multidimensional local limit theorem in deterministic systems and an application to non-convergence of polynomial multiple averages 确定性系统中的多维局部极限定理及其在多项式多重平均不收敛中的应用

arXiv - MATH - Probability Pub Date : 2024-09-08 DOI: arxiv-2409.05087

Zemer Kosloff, Shrey Sanadhya

引用次数: 0

Approximation of birth-death processes 出生-死亡过程的近似值

arXiv - MATH - Probability Pub Date : 2024-09-08 DOI: arxiv-2409.05018

Liping Li

{"title":"Approximation of birth-death processes","authors":"Liping Li","doi":"arxiv-2409.05018","DOIUrl":"https://doi.org/arxiv-2409.05018","url":null,"abstract":"The birth-death process is a special type of continuous-time Markov chain\u0000with index set $mathbb{N}$. Its resolvent matrix can be fully characterized by\u0000a set of parameters $(gamma, beta, nu)$, where $gamma$ and $beta$ are\u0000non-negative constants, and $nu$ is a positive measure on $mathbb{N}$. By\u0000employing the Ray-Knight compactification, the birth-death process can be\u0000realized as a c`adl`ag process with strong Markov property on the one-point\u0000compactification space $overline{mathbb{N}}_{partial}$, which includes an\u0000additional cemetery point $partial$. In a certain sense, the three parameters\u0000that determine the birth-death process correspond to its killing, reflecting,\u0000and jumping behaviors at $infty$ used for the one-point compactification,\u0000respectively. In general, providing a clear description of the trajectories of a\u0000birth-death process, especially in the pathological case where $|nu|=infty$,\u0000is challenging. This paper aims to address this issue by studying the\u0000birth-death process using approximation methods. Specifically, we will\u0000approximate the birth-death process with simpler birth-death processes that are\u0000easier to comprehend. For two typical approximation methods, our main results\u0000establish the weak convergence of a sequence of probability measures, which are\u0000induced by the approximating processes, on the space of all c`adl`ag\u0000functions. This type of convergence is significantly stronger than the\u0000convergence of transition matrices typically considered in the theory of\u0000continuous-time Markov chains.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212151","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

Ordinary and logarithmical convexity of moment generating function 矩生成函数的普通凸性和对数凸性

arXiv - MATH - Probability Pub Date : 2024-09-08 DOI: arxiv-2409.05085

M. R. Formica, E. Ostrovsky, L. Sirota

引用次数: 0

Limit theorems under heavy-tailed scenario in the age dependent random connection models 年龄相关随机连接模型重尾情况下的极限定理

arXiv - MATH - Probability Pub Date : 2024-09-08 DOI: arxiv-2409.05226

Christian Hirsch, Takashi Owada

引用次数: 0

On the expected absorption times of sticky random walks and multiple players war games 论粘性随机漫步和多人战争博弈的预期吸收时间

arXiv - MATH - Probability Pub Date : 2024-09-08 DOI: arxiv-2409.05201

Axel Adjei, Elchanan Mossel

引用次数: 0

Moments of traces of random symplectic matrices and hyperelliptic $L$-functions 随机交映矩阵和超椭圆 $L$ 函数的迹矩

arXiv - MATH - Probability Pub Date : 2024-09-07 DOI: arxiv-2409.04844

Alexei Entin, Noam Pirani

引用次数: 0

Weighted Sub-fractional Brownian Motion Process: Properties and Generalizations 加权亚分数布朗运动过程：性质与概括

arXiv - MATH - Probability Pub Date : 2024-09-07 DOI: arxiv-2409.04798

Ramirez-Gonzalez Jose Hermenegildo, Sun Ying

{"title":"Weighted Sub-fractional Brownian Motion Process: Properties and Generalizations","authors":"Ramirez-Gonzalez Jose Hermenegildo, Sun Ying","doi":"arxiv-2409.04798","DOIUrl":"https://doi.org/arxiv-2409.04798","url":null,"abstract":"In this paper, we present several path properties, simulations, inferences,\u0000and generalizations of the weighted sub-fractional Brownian motion. A primary\u0000focus is on the derivation of the covariance function $R_{f,b}(s,t)$ for the\u0000weighted sub-fractional Brownian motion, defined as: begin{equation*}\u0000R_{f,b}(s,t) = frac{1}{1-b} int_{0}^{s wedge t} f(r) left[(s-r)^{b} +\u0000(t-r)^{b} - (t+s-2r)^{b}right] dr, end{equation*} where $f:mathbb{R}_{+} to\u0000mathbb{R}_{+}$ is a measurable function and $bin [0,1)cup(1,2]$. This\u0000covariance function $R_{f,b}(s,t)$ is used to define the centered Gaussian\u0000process $zeta_{t,f,b}$, which is the weighted sub-fractional Brownian motion.\u0000Furthermore, if there is a positive constant $c$ and $a in (-1,infty)$ such\u0000that $0 leq f(u) leq c u^{a}$ on $[0,T]$ for some $T>0$. Then, for $b in\u0000(0,1)$, $zeta_{t,f,b}$ exhibits infinite variation and zero quadratic\u0000variation, making it a non-semi-martingale. On the other hand, for $b in\u0000(1,2]$, $zeta_{t,f,b}$ is a continuous process of finite variation and thus a\u0000semi-martingale and for $b=0$ the process $zeta_{t,f,0}$ is a square\u0000integrable continuous martingale. We also provide inferential studies using\u0000maximum likelihood estimation and perform simulations comparing various\u0000numerical methods for their efficiency in computing the finite-dimensional\u0000distributions of $zeta_{t,f,b}$. Additionally, we extend the weighted\u0000sub-fractional Brownian motion to $mathbb{R}^d$ by defining new covariance\u0000structures for measurable, bounded sets in $mathbb{R}^d$. Finally, we define a\u0000stochastic integral with respect to $zeta_{t,f,b}$ and introduce both the\u0000weighted sub-fractional Ornstein-Uhlenbeck process and the geometric weighted\u0000sub-fractional Brownian motion.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212154","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

Cumulants in rectangular finite free probability and beta-deformed singular values 矩形有限自由概率中的累积量和β变形奇异值

arXiv - MATH - Probability Pub Date : 2024-09-06 DOI: arxiv-2409.04305

Cesar Cuenca

引用次数: 0