Scaling limits of growth in random media

扩大随机介质的增长极限

基本信息

批准号：
2246576
负责人：
Ivan Corwin
金额：
$ 50万
依托单位：
Columbia University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2023
资助国家：
美国
起止时间：
2023-07-01 至 2028-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2246576&HistoricalAwards=false
关键词：
Scaling limits growth random media

项目摘要

Probability, as a field, tries to address the question of how large complex random systems behave. An important class of probabilistic models deals with growth in random media. These can be used to model how a cancer grows in a particular organ, how a car moves through traffic on a highway, how neurons move through the brain, or how disease moves through a population. The purpose of this project is to understand important models for growth in random media, both in terms of developing statistical distributions associated with the models and in terms of understanding in what sort of systems these models are relevant. The project will leverage new tools to solve previously inaccessible problems. The project includes a range of broader impact activities, including the organization of scientific, education, diversity/equity/inclusion, and outreach programs; advising and mentoring junior researchers; and serving on editorial and scientific boards and committees. Stochastic PDEs, random walks in random media, interacting particle systems, six vertex model, and Gibbs states are active areas of study within probability, equilibrium and non-equilibrium statistical physics, combinatorics, analysis and representation theory. This project touches on problems in and draws upon tools from each of these areas. In particular, this project will probe (1) the nature of invariant measures and mixing times for various growth models in contact with boundaries, (2) the behavior of multi-class particle systems and the propagation of perturbations in growth dynamics, and (3) the fluctuations of interfaces, in particular the likelihood of upper and lower deviation probabilities along with various applications. By marrying integrable structures (e.g. Yang-Baxter equation, symmetric functions, determinantal processes, matrix product ansastz) with probabilistic methods (e.g. couplings, Gibbsian properties, hydrodynamic / stochastic PDE limits) the PI will solve problems in both areas which were previously inaccessible from either approach alone.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.

作为一个领域的概率，试图解决大型复杂随机系统行为的问题。一类重要的概率模型涉及随机培养基中的增长。这些可用于模拟特定器官中癌症的生长，汽车如何通过高速公路上的交通移动，神经元如何在大脑中移动或疾病如何在人群中移动。该项目的目的是了解随机媒体增长的重要模型，无论是开发与模型相关的统计分布以及在这些模型哪种系统中相关的统计分布方面。该项目将利用新工具来解决以前无法访问的问题。该项目包括一系列更广泛的影响活动，包括科学，教育，多样性/公平/包容性和外展计划的组织；为初级研究人员提供建议和指导；并在社论和科学委员会和委员会中任职。随机PDE，随机介质，相互作用的粒子系统，六个顶点模型和吉布斯状态是概率，平衡和非平衡统计物理学，组合术，分析和代表理论的活跃领域。该项目涉及问题，并利用了每个领域的工具。特别是，该项目将探测（1）与边界接触的各种增长模型的不变度度量和混合时间的性质，（2）多级粒子系统的行为以及生长动力学中扰动的传播，以及（3）界面的波动，尤其是在各种应用程序以及各种应用程序的可能性。通过与概率方法（例如，偶联，Gibbsian特性，流体动力 /随机限制）结合使用可集成的结构（例如杨 - 巴克斯克方程，对称函数，确定过程，矩阵乘积ANSASTZ），PI将在两个领域中解决统计信息。认为值得通过基金会的智力优点和更广泛影响的评论标准来评估值得支持。