权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Asymptotics in Probability: Walks and Graphs, Disordered Measures, and Dynamics

概率论渐进：游走和图、无序测度和动力学

基本信息

批准号：
1954337
负责人：
Amir Dembo
金额：
$ 48万
依托单位：
Stanford University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1954337&HistoricalAwards=false
关键词：
Asymptotics Probability Walks Graphs Disordered

项目摘要

Networks and graphs are ubiquitous mathematical models to describe real world systems (social networks, transportation networks, biological systems, and so on). A network comprises a certain number of objects (referred to as nodes) connected by links of various importance (weights). Analyzing the data of a specific large network is notoriously challenging, but for many reasonable models of large random networks one has efficient algorithms to solve such problems, at least for most of the network likely instances. This project aims at developing our fundamental understanding of such probabilistic models and thereby deriving certain classes of efficient algorithms for them. The project provides research training opportunities for graduate students. The project focuses on various models of sparse random graphs, the simplest being the Erdos-Renyi (independent edges) random graph, with slowly growing, or bounded, average degree. Many statistical inference tasks can be addressed by suitably defined combinatorial optimization problems whose solutions can be recovered from the ground states of suitable Gibbs measures on the underlying graph. This project aims at studying various asymptotic properties of large random graphs as well as natural stochastic evolutions on them, thus gaining understanding of the underlying rich structure of the Gibbs measures for which they are invariant.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.

网络和图是描述真实的世界系统（社交网络、交通网络、生物系统等）的普遍存在的数学模型。一个网络由一定数量的对象（称为节点）组成，这些对象通过具有不同重要性（权重）的链接连接起来。分析特定大型网络的数据是众所周知的挑战，但对于大型随机网络的许多合理模型，人们有有效的算法来解决这些问题，至少对于大多数网络可能的实例。该项目旨在发展我们对这种概率模型的基本理解，从而为它们导出某些类的有效算法。该项目为研究生提供研究培训机会。该项目的重点是稀疏随机图的各种模型，最简单的是Erdos-Renyi（独立边）随机图，具有缓慢增长或有界的平均度。许多统计推断任务可以通过适当定义的组合优化问题来解决，这些问题的解可以从底层图上合适的吉布斯测度的基态恢复。该项目旨在研究大型随机图的各种渐近性质以及它们的自然随机演化，从而了解吉布斯测度的潜在丰富结构，因为它们是不变的。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（8）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Diffusions interacting through a random matrix: universality via stochastic Taylor expansion

通过随机矩阵相互作用的扩散：通过随机泰勒展开的普遍性

DOI：
10.1007/s00440-021-01027-7
发表时间：
2021
期刊：
Probability Theory and Related Fields
影响因子：
2
作者：
Dembo, Amir;Gheissari, Reza
通讯作者：
Gheissari, Reza

Everything is a Race and Nakamoto Always Wins

一切都是一场竞赛，中本聪总是获胜

DOI：
10.1145/3372297.3417290
发表时间：
2020
期刊：
CCS '20: Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security
影响因子：
0
作者：
Dembo, Amir;Kannan, Sreeram;Tas, Ertem Nusret;Tse, David;Viswanath, Pramod;Wang, Xuechao;Zeitouni, Ofer
通讯作者：
Zeitouni, Ofer

Dynamics for Spherical Spin Glasses: Disorder Dependent Initial Conditions

球形旋转玻璃的动力学：无序相关的初始条件