Asymptotics of Positive Temperature Models From Statistical Mechanics

统计力学正温度模型的渐进性

基本信息

  • 批准号:
    2230262
  • 负责人:
  • 金额:
    $ 14.93万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2022
  • 资助国家:
    美国
  • 起止时间:
    2022-07-01 至 2024-06-30
  • 项目状态:
    已结题

项目摘要

This project aims to understand the behavior of large random systems at positive temperature. Examples of such models are given by random three-dimensional stepped surfaces, interacting particles systems, the six-vertex model (used to describe the structure of a thin film of water molecules), and interacting avoiding random walkers (sometimes called line ensembles). Many of these models have remarkable algebraic and combinatorial properties, which makes their study tractable. The main goal of the project is to obtain a detailed description (involving exact mathematical formulas) of the asymptotic behavior of these random systems as their size (volume and/or the number of particles) grows. The project involves three interwined directions of research. The first involves the derivation and asymptotic analysis of joint observables for integrable models in the Kardar-Parisi-Zhang (KPZ) universality class. A distinguished feature of integrable models is that they allow for various exact formulas of different observables. A notorious problem with many of these formulas is that they are difficult to study asymptotically, due to the presence of hard to control cross-terms, and one of the goals of the project is to develop a framework for analyzing these cross-terms. The second direction of the project is to establish universal scaling limits for Gibbsian line ensembles. Various integrable models, such as Hall-Littlewood processes and the log-gamma polymer, naturally carry a structure of a line ensemble and it is expected that these ensembles converge to the parabolic Airy line ensemble (one of the universal scaling limits in the KPZ universality class) -- the project seeks to establish this statement. The third direction of the project is to utilize loop equations to understand the scaling limits of multi-level interacting particle systems, which are discrete analogues of the beta-corners processes from random matrix theory and are related to Jack symmetric functions.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.
该项目旨在了解大型随机系统在正温度下的行为。这类模型的例子有随机三维阶梯表面、相互作用粒子系统、六顶点模型(用于描述水分子薄膜的结构)和相互作用避免随机游动(有时称为线系综)。这些模型中的许多具有显著的代数和组合性质,这使得它们的研究易于处理。该项目的主要目标是获得这些随机系统的渐近行为的详细描述(包括精确的数学公式),因为它们的大小(体积和/或粒子数)的增长。 这个项目涉及三个相互交织的研究方向。第一个是Kardar-Parisi-Zhang(KPZ)普适类中可积模型的联合观测量的推导和渐近分析。可积模型的一个显著特征是它们允许不同观测量的各种精确公式。许多这些公式的一个臭名昭著的问题是,由于存在难以控制的交叉项,它们很难渐近地研究,该项目的目标之一是开发一个分析这些交叉项的框架。该项目的第二个方向是为Gibbsian线合奏建立通用的缩放限制。各种可积模型,如Hall-Littlewood过程和log-gamma聚合物,自然带有线系综的结构,预计这些系综会收敛到抛物线艾里线系综(KPZ普适性类中的通用尺度限制之一)-该项目试图建立这一声明。该项目的第三个方向是利用循环方程来理解多层次相互作用粒子系统的尺度限制,这是随机矩阵理论中β角过程的离散模拟,与Jack对称函数有关。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

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Evgeni Dimitrov其他文献

Multi-level loop equations for $$\beta $$ -corners processes
  • DOI:
    10.1007/s00029-024-01006-5
  • 发表时间:
    2024-12-16
  • 期刊:
  • 影响因子:
    1.200
  • 作者:
    Evgeni Dimitrov;Alisa Knizel
  • 通讯作者:
    Alisa Knizel
Large deviations for discrete emβ/em-ensembles
离散 emβ 系综的大偏差
  • DOI:
    10.1016/j.jfa.2022.109487
  • 发表时间:
    2022-07-01
  • 期刊:
  • 影响因子:
    1.600
  • 作者:
    Sayan Das;Evgeni Dimitrov
  • 通讯作者:
    Evgeni Dimitrov
A pandemic recap: lessons we have learned
  • DOI:
    10.1186/s13017-021-00393-w
  • 发表时间:
    2021-09-10
  • 期刊:
  • 影响因子:
    5.800
  • 作者:
    Federico Coccolini;Enrico Cicuttin;Camilla Cremonini;Dario Tartaglia;Bruno Viaggi;Akira Kuriyama;Edoardo Picetti;Chad Ball;Fikri Abu-Zidan;Marco Ceresoli;Bruno Turri;Sumita Jain;Carlo Palombo;Xavier Guirao;Gabriel Rodrigues;Mahir Gachabayov;Fernando Machado;Lostoridis Eftychios;Souha S. Kanj;Isidoro Di Carlo;Salomone Di Saverio;Vladimir Khokha;Andrew Kirkpatrick;Damien Massalou;Francesco Forfori;Francesco Corradi;Samir Delibegovic;Gustavo M. Machain Vega;Massimo Fantoni;Demetrios Demetriades;Garima Kapoor;Yoram Kluger;Shamshul Ansari;Ron Maier;Ari Leppaniemi;Timothy Hardcastle;Andras Vereczkei;Evika Karamagioli;Emmanouil Pikoulis;Mauro Pistello;Boris E. Sakakushev;Pradeep H. Navsaria;Rita Galeiras;Ali I. Yahya;Aleksei V. Osipov;Evgeni Dimitrov;Krstina Doklestić;Michele Pisano;Paolo Malacarne;Paolo Carcoforo;Maria Grazia Sibilla;Igor A. Kryvoruchko;Luigi Bonavina;Jae Il Kim;Vishal G. Shelat;Jacek Czepiel;Emilio Maseda;Sanjay Marwah;Mircea Chirica;Giandomenico Biancofiore;Mauro Podda;Lorenzo Cobianchi;Luca Ansaloni;Paola Fugazzola;Charalampos Seretis;Carlos Augusto Gomez;Fabio Tumietto;Manu Malbrain;Martin Reichert;Goran Augustin;Bruno Amato;Alessandro Puzziello;Andreas Hecker;Angelo Gemignani;Arda Isik;Alessandro Cucchetti;Mirco Nacoti;Doron Kopelman;Cristian Mesina;Wagih Ghannam;Offir Ben-Ishay;Sameer Dhingra;Raul Coimbra;Ernest E. Moore;Yunfeng Cui;Martha A. Quiodettis;Miklosh Bala;Mario Testini;Jose Diaz;Massimo Girardis;Walter L. Biffl;Matthias Hecker;Ibrahima Sall;Ugo Boggi;Gabriele Materazzi;Lorenzo Ghiadoni;Junichi Matsumoto;Wietse P. Zuidema;Rao Ivatury;Mushira A. Enani;Andrey Litvin;Majdi N. Al-Hasan;Zaza Demetrashvili;Oussama Baraket;Carlos A. Ordoñez;Ionut Negoi;Ronald Kiguba;Ziad A. Memish;Mutasim M. Elmangory;Matti Tolonen;Korey Das;Julival Ribeiro;Donal B. O’Connor;Boun Kim Tan;Harry Van Goor;Suman Baral;Belinda De Simone;Davide Corbella;Pietro Brambillasca;Michelangelo Scaglione;Fulvio Basolo;Nicola De’Angelis;Cino Bendinelli;Dieter Weber;Leonardo Pagani;Cinzia Monti;Gianluca Baiocchi;Massimo Chiarugi;Fausto Catena;Massimo Sartelli
  • 通讯作者:
    Massimo Sartelli
Study of the hydrogen influence on the combustion parameters of diesel engine
关于氢对柴油机燃烧参数影响的研究
  • DOI:
    10.1016/j.ijhydene.2025.02.114
  • 发表时间:
    2025-04-29
  • 期刊:
  • 影响因子:
    8.300
  • 作者:
    Evgeni Dimitrov;Mihail Peychev;Atanasi Tashev
  • 通讯作者:
    Atanasi Tashev
Questionable risk-benefit ratio of adjuvant therapy in stage II colorectal cancer due to the lack of validated stratification factors for the selection of patients
  • DOI:
    10.1016/j.ejso.2023.107640
  • 发表时间:
    2024-02-01
  • 期刊:
  • 影响因子:
  • 作者:
    Emil Enchev;Evgeni Dimitrov;Georgi Minkov;Ivan Dimitrov;Alen Petrov;Yovcho Yovchev
  • 通讯作者:
    Yovcho Yovchev

Evgeni Dimitrov的其他文献

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{{ truncateString('Evgeni Dimitrov', 18)}}的其他基金

Asymptotics of Positive Temperature Models From Statistical Mechanics
统计力学正温度模型的渐进性
  • 批准号:
    2054703
  • 财政年份:
    2021
  • 资助金额:
    $ 14.93万
  • 项目类别:
    Standard Grant

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阐明等离激元带激发下金纳米粒子周围的不均匀温度分布所发挥的积极作用
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    22K04884
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Rigorous coarse-graining of defects at positive temperature
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Asymptotics of Positive Temperature Models From Statistical Mechanics
统计力学正温度模型的渐进性
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    2021
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    $ 14.93万
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    Standard Grant
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正温度下布朗运动和随机交错相互作用系统的大偏差分析
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