Heat Kernels and Geometries in Discrete and Continuous Settings

离散和连续设置中的热核和几何形状

基本信息

  • 批准号:
    2054593
  • 负责人:
  • 金额:
    $ 38.5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2021
  • 资助国家:
    美国
  • 起止时间:
    2021-07-15 至 2024-06-30
  • 项目状态:
    已结题

项目摘要

Models of human activities often involve randomness. Randomness is used to understand DNA, image restoration and recognition, communication and social networks, and the behavior of financial markets. It is an important tool for efficient computations and for scientific simulations. In all these applications, the behavior of the model's random process is constrained by the combinatorial or geometric structure underlying the system under study. This project is concerned with the fundamental properties of such stochastic processes and how they relate to the global geometric structure of their environment, be it discrete or continuous. The project provides training opportunities for graduate students. The project focuses on random processes that are defined by a related geometric or algebraic structure. The global behaviors of these processes are determined by this global structure. In some cases, these behaviors are useful to obtain information on the underlying space. This research lies at the interface between analysis, geometry, and probability, with the notion of group playing a key part. Partial differential equations and potential theory, i.e., the study of harmonic functions and solutions of the heat equation, are also at the center of many of these considerations. Brownian motion on a Riemannian manifold and random walks on Cayley graphs of finitely generated groups provide key examples.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.
人类活动的模型经常包含随机性。随机性被用来理解DNA,图像恢复和识别,通信和社会网络,以及金融市场的行为。它是进行高效计算和科学模拟的重要工具。在所有这些应用中,模型随机过程的行为受到所研究系统的组合结构或几何结构的约束。该项目关注这些随机过程的基本特性,以及它们与环境的全局几何结构的关系,无论是离散的还是连续的。该项目为研究生提供了培训机会。该项目侧重于由相关几何或代数结构定义的随机过程。这些流程的全局行为由这个全局结构决定。在某些情况下,这些行为对于获取有关底层空间的信息很有用。本研究处于分析、几何和概率论的交叉点,群的概念起着关键作用。偏微分方程和势理论,即对调和函数和热方程解的研究,也是许多这些考虑的中心。黎曼流形上的布朗运动和有限生成群的Cayley图上的随机游走提供了关键的例子。该奖项反映了美国国家科学基金会的法定使命,并通过使用基金会的知识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(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Long range random walks and associated geometries on groups of polynomial growth
多项式增长组上的长程随机游走和相关几何
  • DOI:
    10.5802/aif.3515
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Chen, Zhen-Qing;Kumagai, Takashi;Saloff-Coste, Laurent;Wang, Jian;Zheng, Tianyi
  • 通讯作者:
    Zheng, Tianyi
On-diagonal asymptotics for heat kernels of a class of inhomogeneous partial differential operators
  • DOI:
    10.1016/j.jde.2023.03.011
  • 发表时间:
    2022-06
  • 期刊:
  • 影响因子:
    2.4
  • 作者:
    Evan Randles;L. Saloff‐Coste
  • 通讯作者:
    Evan Randles;L. Saloff‐Coste
Perturbation results concerning Gaussian estimates and hypoellipticity for left-invariant Laplacians on compact groups
关于紧群上左不变拉普拉斯的高斯估计和亚椭圆性的扰动结果
  • DOI:
    10.4064/cm8696-8-2022
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0.4
  • 作者:
    Hou, Qi;Saloff-Coste, Laurent
  • 通讯作者:
    Saloff-Coste, Laurent
Book Review: Potential theory and geometry on Lie groups
书评:李群的势理论和几何
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Laurent Saloff-Coste其他文献

Bounds for Kac's Master Equation
  • DOI:
    10.1007/s002200050036
  • 发表时间:
    2000-02-01
  • 期刊:
  • 影响因子:
    2.600
  • 作者:
    Persi Diaconis;Laurent Saloff-Coste
  • 通讯作者:
    Laurent Saloff-Coste
Inequalities forp-superharmonic functions on networks
  • DOI:
    10.1007/bf02925256
  • 发表时间:
    1995-12-01
  • 期刊:
  • 影响因子:
    0.800
  • 作者:
    Laurent Saloff-Coste
  • 通讯作者:
    Laurent Saloff-Coste
Parabolic Harnack inequality for divergence form second order differential operators
  • DOI:
    10.1007/978-94-011-0085-4_9
  • 发表时间:
    1995-08
  • 期刊:
  • 影响因子:
    1.1
  • 作者:
    Laurent Saloff-Coste
  • 通讯作者:
    Laurent Saloff-Coste
Some Inequalities for Superharmonic Functions on Graphs
  • DOI:
    10.1023/a:1008648421123
  • 发表时间:
    1997-01-01
  • 期刊:
  • 影响因子:
    0.800
  • 作者:
    Laurent Saloff-Coste
  • 通讯作者:
    Laurent Saloff-Coste
On the Convolution Powers of Complex Functions on $$\mathbb {Z}$$

Laurent Saloff-Coste的其他文献

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{{ truncateString('Laurent Saloff-Coste', 18)}}的其他基金

Diffusions and jump processes on groups and manifolds
群和流形上的扩散和跳跃过程
  • 批准号:
    2343868
  • 财政年份:
    2024
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Continuing Grant
Random Walks and Diffusions and Their Geometries
随机游走和扩散及其几何
  • 批准号:
    1707589
  • 财政年份:
    2017
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Standard Grant
Random walks, diffusions, semigroups, and associated geometries
随机游走、扩散、半群和相关几何
  • 批准号:
    1404435
  • 财政年份:
    2014
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Continuing Grant
Asymptotically Efficient and Efficiently Computable Bayesian Estimation
渐近有效且高效可计算的贝叶斯估计
  • 批准号:
    1406599
  • 财政年份:
    2014
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Continuing Grant
US participant support for the Instut Henri Poincare quarter program "Random Walks and the Asymptotic Geometry of Groups"
美国参与者支持 Instut Henri Poincare 季度项目“随机游走和群的渐近几何”
  • 批准号:
    1344959
  • 财政年份:
    2013
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Standard Grant
Heat kernel estimates and applications
热核估计和应用
  • 批准号:
    1004771
  • 财政年份:
    2010
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Continuing Grant
Travel Grants for US Participants, SPA Berlin 2009 33rd Conference on Stochastic Processes and Their Applications
为美国参与者提供旅费资助,2009 年柏林 SPA 第 33 届随机过程及其应用会议
  • 批准号:
    0855857
  • 财政年份:
    2009
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Standard Grant
EMSW21-RTG: Interdisciplinary Training in the Applications of Probability
EMSW21-RTG:概率应用的跨学科培训
  • 批准号:
    0739164
  • 财政年份:
    2008
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Continuing Grant
Markov Processes in Geometric Environments
几何环境中的马尔可夫过程
  • 批准号:
    0603886
  • 财政年份:
    2006
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Continuing Grant
Analysis and Geometry of Markov Chains Diffusion Processes
马尔可夫链扩散过程的分析与几何
  • 批准号:
    0102126
  • 财政年份:
    2001
  • 资助金额:
    $ 38.5万
  • 项目类别:
    Continuing Grant

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  • 批准号:
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