Random walks, diffusions, semigroups, and associated geometries
随机游走、扩散、半群和相关几何
基本信息
- 批准号:1404435
- 负责人:
- 金额:$ 33万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2014
- 资助国家:美国
- 起止时间:2014-07-01 至 2018-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Random processes play an important role in many aspects of science and other human activities. The study of card shuffling procedures provides an entertaining yet complex and mathematically interesting example. It also serves as a model for the many important mixing phenomena. We use randomness to understand complex phenomena, from the behavior of polymer molecules and DNA analysis, to image restoration and recognition, communication and social networks, and the behavior of financial markets. Random processes are also used as important tools for efficient computations. In all these cases, there are strong structural constraints underlying the behavior of the relevant random process. These constraints are expressed in terms of the environment of the process which often has a complex combinatorial or geometric structure. This proposal focuses on the study of the fundamental properties of such stochastic processes and on how they relate to the global structure of their environment.Many basic Markov processes evolve on a state space carrying a related geometric structure. Brownian motion on a Riemannian manifold, random walks on Cayley graphs of finitely generated groups and finite Markov chains on complex combinatorial structures such as trees or matchings are significant examples. This proposal focuses on the relationships between the behavior of such processes and the properties of the underlying geometric structure. It involves problems at the interface between analysis, geometry and probability with a major role played by groups and their actions. Potential theory, i.e., the study of harmonic functions and, more generally, of solutions of the heat equation, is also at the center of many of these considerations.
随机过程在科学和其他人类活动的许多方面都扮演着重要的角色。洗牌程序的研究提供了一个有趣但复杂的数学有趣的例子。它也是许多重要混合现象的模型。我们使用随机性来理解复杂的现象,从聚合物分子的行为和DNA分析,到图像恢复和识别、通信和社交网络,以及金融市场的行为。随机过程也被用作有效计算的重要工具。在所有这些情况下,相关随机过程的行为背后都有很强的结构性约束。这些约束是根据过程的环境来表示的,该过程往往具有复杂的组合或几何结构。研究了这类随机过程的基本性质以及它们与环境的全局结构之间的关系。许多基本马尔可夫过程都是在带有相关几何结构的状态空间上演化的。黎曼流形上的布朗运动,有限生成群的Cayley图上的随机游动,以及树或匹配等复杂组合结构上的有限马氏链都是重要的例子。这项建议侧重于这些过程的行为和基本几何结构的属性之间的关系。它涉及分析、几何和概率之间的界面问题,其中群体及其行动扮演着主要角色。位势理论,即研究调和函数,以及更广泛地说,研究热方程的解,也是许多这些考虑的中心。
项目成果
期刊论文数量(5)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Positive-Homogeneous Operators, Heat Kernel Estimates and the Legendre-Fenchel Transform
正齐次算子、热核估计和勒让德-芬切尔变换
- DOI:10.1007/978-3-319-59671-6
- 发表时间:2017
- 期刊:
- 影响因子:0
- 作者:Randles, Evan;Saloff-Coste, Laurent
- 通讯作者:Saloff-Coste, Laurent
Random walks and isoperimetric profiles under moment conditions
矩条件下的随机游走和等周剖面
- DOI:10.1214/15-aop1070
- 发表时间:2016
- 期刊:
- 影响因子:0
- 作者:Saloff-Coste, Laurent;Zheng, Tianyi
- 通讯作者:Zheng, Tianyi
Heat kernel estimates on connected sums of parabolic manifolds
抛物流形连通和的热核估计
- DOI:10.1016/j.matpur.2018.03.002
- 发表时间:2018
- 期刊:
- 影响因子:0
- 作者:Grigor'yan, Alexander;Ishiwata, Satoshi;Saloff-Coste, Laurent
- 通讯作者:Saloff-Coste, Laurent
Convolution powers of complex functions on $\mathbb Z^d$
$mathbb Z^d$ 上复函数的卷积幂
- DOI:10.4171/rmi/964
- 发表时间:2017
- 期刊:
- 影响因子:0
- 作者:Randles, Evan;Saloff-Coste, Laurent
- 通讯作者:Saloff-Coste, Laurent
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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
On the Convolution Powers of Complex Functions on $$\mathbb {Z}$$
- DOI:
10.1007/s00041-015-9386-1 - 发表时间:
2015-03-07 - 期刊:
- 影响因子:1.200
- 作者:
Evan Randles;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
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:
$ 33万 - 项目类别:
Continuing Grant
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
- 批准号:
2054593 - 财政年份:2021
- 资助金额:
$ 33万 - 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:
$ 33万 - 项目类别:
Standard 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:
$ 33万 - 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:
$ 33万 - 项目类别:
Standard 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:
$ 33万 - 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:
$ 33万 - 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:
$ 33万 - 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:
$ 33万 - 项目类别:
Continuing Grant
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CRII:FET:离散量子行走的量子优势
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随机游走的并行化和鲁棒性:“短”随机游走分析的方法
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23K16840 - 财政年份:2023
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RUI: Boundary and entropy of random walks on groups
RUI:群体随机游走的边界和熵
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2246727 - 财政年份:2023
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迭代函数方案、动力系统和随机游走的经过验证的数值
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