Random functions and stochastic processes on random graphs

随机图上的随机函数和随机过程

• 批准号: 2246575
• 负责人: Oanh Nguyen
• 金额: $ 18万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2026-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2246575&HistoricalAwards=false
• 关键词: Random; functions; stochastic; processes; random

The analysis of roots of polynomials with random coefficients is a growing area with applications in subfields across mathematics, including approximation theory, mathematical physics, and ordinary differential equations. This project will investigate various features of the distribution of the number of roots. Another focus of this project is the contact process on random networks, aiming to understand the dynamics of contagion as it spreads through complex interconnected systems. This work will provide insight into real-world epidemics and information dissemination, leading to the development of more effective strategies for controlling and preventing the spread of infections or ideas. This research project seeks to deepen our understanding of these ubiquitous random structures and to explore their applications in real-world problems. Graduate and undergraduate students will be mentored as part of this project, and the research findings will be disseminated through publications and research talks, reaching a wide audience.More specifically, this research project will investigate the universality of variances and higher moments of the number of real roots, along with the asymptotic distribution of this number. To achieve this, various universality techniques will be used to develop new tools and connections. Regarding the contact process, the project specifically focuses on the susceptible-infected-susceptible (SIS) model and will explore the phase transition of the survival time. Novel ideas and methods will be pursued to rigorously analyze the SIS contact process. Through these projects, new connections between different areas are anticipated to emerge, leading to fresh insights and applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

与随机系数的多项式的根对根的分析是一个生长区域，在数学跨越子场中应用，包括近似理论，数学物理学和普通的微分方程。该项目将调查根部分布的各种特征。该项目的另一个重点是随机网络上的接触过程，旨在了解传播通过复杂的互连系统传播时的动态。这项工作将提供对现实世界流行病和信息传播的见解，从而制定了控制和防止感染或思想传播的更有效的策略。该研究项目旨在加深我们对这些普遍存在的随机结构的理解，并探索它们在现实世界中的应用。 研究生和本科生将作为该项目的一部分进行指导，研究结果将通过出版物和研究演讲传播，吸引广泛的受众群体。更具体地说，该研究项目将调查差异的普遍性和实际根源数量的较高时刻，以及该数量的渐近分布。为此，将使用各种普遍性技术来开发新的工具和连接。关于接触过程，该项目专门针对易感感染感染的（SIS）模型，并将探索生存时间的相变。新颖的想法和方法将被追求严格分析SIS接触过程。通过这些项目，预计不同领域之间的新联系将出现，从而带来了新的见解和应用。该奖项反映了NSF的法定任务，并且使用基金会的知识分子优点和更广泛的审查标准，被认为值得通过评估来获得支持。