Scaling Limits of Growth in Random Media

扩大随机介质的生长极限

基本信息

  • 批准号:
    1811143
  • 负责人:
  • 金额:
    $ 50万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2018
  • 资助国家:
    美国
  • 起止时间:
    2018-07-01 至 2025-06-30
  • 项目状态:
    未结题

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 deal 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 spreads 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 tools that the PI has been developing from a number of areas of mathematics to solve problems which were previously inaccessible.Stochastic partial differential equations, random walks in random media, interacting particle systems, six vertex model, and Gibbs states are active areas of study within probability, equilibrium / non-equilibrium statistics 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 (1) Develop a new Markov duality based method to prove convergence of microscopic models (including the six vertex model, dynamic ASEP and ASEP with inhomogeneous jump rates) to the KPZ equation, (2) Prove tail and large deviation bounds on the KPZ equation and related processes, and use these for applications like the slow bond problem, (3) Study scaling behavior for random walks in random environments and develop relationships between the FKPP and KPZ equations, as well as study the uniqueness of Gibbsian line ensembles. Through marrying methods from integrable probability and stochastic analysis, 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.
概率作为一个领域,试图解决大型复杂随机系统如何表现的问题。一类重要的概率模型处理随机介质中的增长。这些可以用来模拟癌症如何在特定器官中生长,汽车如何在高速公路上的交通中移动,神经元如何在大脑中移动,或者疾病如何在人群中传播。该项目的目的是了解随机介质中增长的重要模型,包括与模型相关的统计分布,以及了解这些模型与什么样的系统相关。该项目将利用PI从许多数学领域开发的工具来解决以前无法解决的问题。随机偏微分方程,随机介质中的随机行走,相互作用粒子系统,六顶点模型和吉布斯状态是概率,平衡/非平衡统计物理,组合学,分析和表示论的活跃研究领域。这个项目涉及到这些领域的问题,并借鉴了这些领域的工具。特别是,本项目将(1)开发一种新的基于马尔可夫对偶的方法来证明微观模型的收敛性(2)证明KPZ方程及相关过程的尾部和大偏差界,并将其用于慢键问题等应用,(3)研究了随机环境中随机游动的标度行为,建立了FKPP方程与KPZ方程之间的关系,并研究了Gibbsian线系综的唯一性。通过结合可积概率和随机分析的方法,PI将解决这两个领域中以前单独使用任何一种方法都无法解决的问题。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的评估被认为值得支持影响审查标准。

项目成果

期刊论文数量(27)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Stochastic PDE limit of the dynamic ASEP
动态 ASEP 的随机 PDE 极限
  • DOI:
    10.1007/s00220-020-03905-y
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    2.4
  • 作者:
    Corwin, Ivan;Ghosal, Promit;Matetski, Konstantin
  • 通讯作者:
    Matetski, Konstantin
Large deviations for sticky Brownian motions
  • DOI:
    10.1214/20-ejp515
  • 发表时间:
    2019-05
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Guillaume Barraquand;M. Rychnovsky
  • 通讯作者:
    Guillaume Barraquand;M. Rychnovsky
Francis Comets’ Gumbel last passage percolation
弗朗西斯·科梅茨 (Francis Comet) 甘贝尔最后一段渗透
Lower tail of the KPZ equation
KPZ 方程的下尾部
  • DOI:
    10.1215/00127094-2019-0079
  • 发表时间:
    2020
  • 期刊:
  • 影响因子:
    2.5
  • 作者:
    Corwin, Ivan;Ghosal, Promit
  • 通讯作者:
    Ghosal, Promit
Some Recent Progress on the Stationary Measure for the Open KPZ Equation
开KPZ方程平稳测度的一些新进展
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Ivan Corwin其他文献

The q-Hahn Boson Process and q-Hahn TASEP
q-Hahn 玻色子过程和 q-Hahn TASEP
  • DOI:
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Ivan Corwin
  • 通讯作者:
    Ivan Corwin
Exactly solving the KPZ equation
Harold Widom’s work in random matrix theory
Harold Widom 在随机矩阵理论方面的工作
Time Inconsistency and Uncertainty Aversion in Prediction Markets
预测市场中的时间不一致和不确定性厌恶
  • DOI:
  • 发表时间:
    2008
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Ivan Corwin;Abraham Othman
  • 通讯作者:
    Abraham Othman
A Classical Limit of Noumi's q-Integral Operator
Noumi q-积分算子的经典极限
  • DOI:
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    A. Borodin;Ivan Corwin;Daniel Remenik
  • 通讯作者:
    Daniel Remenik

Ivan Corwin的其他文献

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{{ truncateString('Ivan Corwin', 18)}}的其他基金

Scaling limits of growth in random media
扩大随机介质的增长极限
  • 批准号:
    2246576
  • 财政年份:
    2023
  • 资助金额:
    $ 50万
  • 项目类别:
    Continuing Grant
Workshop on Transport and Localization in Random Media: Theory and Applications
随机媒体传输和定位研讨会:理论与应用
  • 批准号:
    1804339
  • 财政年份:
    2018
  • 资助金额:
    $ 50万
  • 项目类别:
    Standard Grant
CBMS Conference: Dyson-Schwinger Equations, Topological Expansions, and Random Matrices
CBMS 会议:Dyson-Schwinger 方程、拓扑展开式和随机矩阵
  • 批准号:
    1642595
  • 财政年份:
    2017
  • 资助金额:
    $ 50万
  • 项目类别:
    Standard Grant
FRG: Collaborative Research: Integrable Probability
FRG:协作研究:可积概率
  • 批准号:
    1664650
  • 财政年份:
    2017
  • 资助金额:
    $ 50万
  • 项目类别:
    Continuing Grant
Conference on Quantum Integrable Systems, Conformal Field Theories and Stochastic Processes
量子可积系统、共形场论和随机过程会议
  • 批准号:
    1637087
  • 财政年份:
    2016
  • 资助金额:
    $ 50万
  • 项目类别:
    Standard Grant
Exact solvability of the Kardar-Parisi-Zhang stochastic partial differential equation
Kardar-Parisi-Zhang 随机偏微分方程的精确可解性
  • 批准号:
    1438867
  • 财政年份:
    2014
  • 资助金额:
    $ 50万
  • 项目类别:
    Standard Grant
Exact solvability of the Kardar-Parisi-Zhang stochastic partial differential equation
Kardar-Parisi-Zhang 随机偏微分方程的精确可解性
  • 批准号:
    1208998
  • 财政年份:
    2012
  • 资助金额:
    $ 50万
  • 项目类别:
    Standard Grant

相似海外基金

Scaling limits of growth in random media
扩大随机介质的增长极限
  • 批准号:
    2246576
  • 财政年份:
    2023
  • 资助金额:
    $ 50万
  • 项目类别:
    Continuing Grant
Genomic factors contributing to the upper temperature growth limits of bacteria
影响细菌温度生长上限的基因组因素
  • 批准号:
    RGPIN-2018-03747
  • 财政年份:
    2022
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    $ 50万
  • 项目类别:
    Discovery Grants Program - Individual
Genomic factors contributing to the upper temperature growth limits of bacteria
影响细菌温度生长上限的基因组因素
  • 批准号:
    RGPIN-2018-03747
  • 财政年份:
    2021
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Genomic factors contributing to the upper temperature growth limits of bacteria
影响细菌温度生长上限的基因组因素
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    RGPIN-2018-03747
  • 财政年份:
    2020
  • 资助金额:
    $ 50万
  • 项目类别:
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Exploring the limits of real-time studies of growth of molecular and hybrid systems
探索分子和混合系统生长实时研究的局限性
  • 批准号:
    419187842
  • 财政年份:
    2019
  • 资助金额:
    $ 50万
  • 项目类别:
    Research Grants
Genomic factors contributing to the upper temperature growth limits of bacteria
影响细菌温度生长上限的基因组因素
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    RGPIN-2018-03747
  • 财政年份:
    2019
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Limits to population growth of an apex omnivore: Untangling the influences of human predation, competing species and high nutritional requirements.
顶级杂食动物种群增长的限制:阐明人类捕食、物种竞争和高营养需求的影响。
  • 批准号:
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  • 财政年份:
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随机生长和 SLE 限制
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Genomic factors contributing to the upper temperature growth limits of bacteria
影响细菌温度生长上限的基因组因素
  • 批准号:
    RGPIN-2018-03747
  • 财政年份:
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  • 资助金额:
    $ 50万
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Limits to population growth of an apex omnivore: Untangling the influences of human predation, competing species and high nutritional requirements.
顶级杂食动物种群增长的限制:阐明人类捕食、物种竞争和高营养需求的影响。
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