CAREER: Probability on Groups and Semigroups of Probabilities

职业：概率群和半群的概率

• 批准号: 1944153
• 负责人: Omer Tamuz
• 金额: $ 42.5万
• 依托单位: California Institute of Technology
• 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: 2020-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1944153&HistoricalAwards=false
• 关键词: CAREER; Probability; Groups; Semigroups; Probabilities

Probability is a field of mathematics that has wide applications in science, engineering, statistics, economics, philosophy, and every discipline in which uncertainty and randomness play a crucial role. Within probability, we study random walks, which are used to model various physical and economic phenomena, and also have important connections to other fields of mathematics. In this project we explore some long standing mysteries regarding random walks, and in particular are interested in understanding path-dependence: for which random walks do random fluctuations in the beginning have a lasting impact on the long term? A further objective is to explore newly discovered connections to questions in information theory and economics: Which sources of information are more valuable in the long term? And how is information priced? The educational component of this project will include novel research opportunities for undergraduate students, with the aim of attracting promising students to this field by exposing them to modern questions and techniques.The Furstenberg-Poisson boundary of a random walk on a group has been the object of intense study since its introduction in Furstenberg's foundational work in the 1960s and 1970s. This literature is by now mature, with many established connections to neighboring fields. Yet, some compelling basic questions remain open. For example: which groups admit finitely supported random walks with a non-trivial boundary? In this project we hope to leverage recent breakthroughs to advance the state of the art in this field, and in particular to study the so-called "stability conjecture" and "gap conjecture." In the field of topological group actions, the notions of proximality and strong proximality have been the object of a large research effort. Recently, it has been shown that a finitely generated group is virtually nilpotent if and only if all of its proximal actions on compact spaces have fixed points. This establishes a still mysterious connection between proximal actions and the Furstenberg-Poisson boundary, which we plan to explore. Finally, this project will also explore stochastic dominance, which is is an important tool for comparison of distributions in economics and statistics. We will pursue a recently initiated research agenda studying the interaction of stochastic dominance and convolution, with applications to the Blackwell theory of experiments.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.

概率是数学的一个领域，在科学、工程、统计、经济、哲学以及不确定性和随机性发挥关键作用的每一门学科中都有广泛的应用。在概率论中，我们研究随机游走，它被用来模拟各种物理和经济现象，并且与其他数学领域也有重要的联系。在这个项目中，我们将探索一些关于随机游动的长期存在的谜团，特别是对理解路径依赖感兴趣：对于哪些随机游动，开始时的随机波动会对长期产生持久的影响？另一个目标是探索新发现的与信息理论和经济学问题的联系：从长远来看，哪些信息来源更有价值？信息如何定价？该项目的教育部分将包括为本科生提供新的研究机会，目的是通过让有前途的学生接触现代问题和技术来吸引他们进入这一领域。群上随机游走的Furstenberg-Poisson边界自20世纪60年代和70年代在Furstenberg的基础工作中引入以来一直是深入研究的对象。这方面的文献到目前为止已经成熟，与邻近领域有许多既定的联系。然而，一些令人信服的基本问题仍然悬而未决。例如：哪些群允许有非平凡边界的可支持随机游动？在这个项目中，我们希望利用最新的突破来推进这一领域的最新技术，特别是研究所谓的“稳定性猜想”和“间隙猜想”。在拓扑群作用领域，邻近性和强邻近性的概念一直是大量研究工作的对象。最近，它已被证明，一个生成群是几乎幂零的，当且仅当它的所有邻近作用在紧空间有不动点。这在近端作用和我们计划探索的Furstenberg-Poisson边界之间建立了一种仍然神秘的联系。最后，本项目还将探讨随机优势，这是经济学和统计学中比较分布的重要工具。我们将继续研究最近启动的研究议程，研究随机优势和卷积的相互作用，并应用于Blackwell实验理论。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

Additive conjugacy and the Bohr compactification of orthogonal representations

加法共轭和正交表示的玻尔紧化

• DOI: 10.1007/s00208-021-02191-w
• 发表时间: 2021
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: Chase, Z.;Hann-Caruthers, W.;Tamuz, O
• 通讯作者: Tamuz, O

The Cost of Information: The Case of Constant Marginal Costs

信息成本：边际成本不变的情况

• DOI: 10.1257/aer.20190185
• 发表时间: 2023
• 期刊: American Economic Review
• 影响因子: 10.7
• 作者: Pomatto, Luciano;Strack, Philipp;Tamuz, Omer
• 通讯作者: Tamuz, Omer

Feasible Joint Posterior Beliefs

可行的联合后验信念

• DOI: 10.1145/3391403.3399505
• 发表时间: 2021
• 期刊: The journal of political economy
• 作者: Arieli, I.;Babichenko, Y.;Sandomirskiy, F.;Tamuz, O
• 通讯作者: Tamuz, O

Characteristic measures of symbolic dynamical systems

符号动力系统的特征测度

• DOI: 10.1017/etds.2021.16
• 发表时间: 2022
• 期刊: Ergodic theory dynamical systems
• 作者: Frischm J.;Tamuz, O.
• 通讯作者: Tamuz, O.

Equitable Voting Rules

公平投票规则

• DOI: 10.3982/ecta17032
• 发表时间: 2021
• 期刊: Econometrica
• 影响因子: 6.1
• 作者: Bartholdi, Laurent;Hann-Caruthers, Wade;Josyula, Maya;Tamuz, Omer;Yariv, Leeat
• 通讯作者: Yariv, Leeat