Random Processes on Graphs, and Planar Brownian Motion
图上的随机过程和平面布朗运动
基本信息
- 批准号:9803597
- 负责人:
- 金额:$ 8.67万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:1998
- 资助国家:美国
- 起止时间:1998-07-01 至 2002-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
9803597 Peres The principal investigator will analyze various random processes on graphs. For instance, a model of noisy propagation on trees has been studied independently in Statistical Mechanics, in Computer Science and in Genetic Reconstruction. This model is well understood only when the propagating variables take two values, when it can be identified with the Ising model. There are two distinct critical temperatures, one for uniqueness of Gibbs states and another for purity of the Markovian state that corresponds to free boundary conditions. The second critical temperature is not known for the Potts model, where the propagating variables can take more than two values. To study large homogeneous graphs that are not trees, the investigator will apply a new "mass transport method" developed recently with several collaborators. Problems on the geometry of the planar Brownian path will also be investigated; a key tool will be the intersection equivalence of the paths with random sets constructed via "fractal percolation". Mathematical biologists studying the spread of genetic mutations in a family tree, and computer scientists studying the propagation of errors in a noisy communication network, were led independently to the same mathematical model that was considered earlier in statistical mechanics. The principal investigator will attempt to unify and extend some of the earlier results on these models, by using recent probabilistic techniques; some of this involves collaboration with computer scientists. Recently, new methods have emerged to exploit symmetries in the geometry of the underlying network, to obtain better understanding of random processes on it; the investigator will develop and apply these methods further. Finally, the trace of the erratic random motion of a particle has been studied intensively by probabilists; this research will investigate certain new approaches to these traces to try and elucidate their geometric structure.
小行星9803597 主要研究者将分析图上的各种随机过程。为 例如,树上的噪声传播模型已独立研究, 统计力学,计算机科学和遗传重建。该模型 只有当传播变量取两个值时才能很好地理解,当它可以 与伊辛模型一致。有两个不同的临界温度,一个是 吉布斯状态的唯一性和另一个对应的马尔可夫状态的纯度 自由边界条件。第二个临界温度是不知道的波茨 模型,其中传播变量可以取两个以上的值。学习大 齐次图不是树,研究人员将应用一个新的“质量运输”, 最近与几位合作者一起开发的“方法”。几何问题 平面布朗路径也将被研究;一个关键的工具将是相交 通过“分形渗流”构造的随机集的路径的等价性。 数学生物学家研究基因突变在家谱中的传播, 计算机科学家研究在嘈杂的通信中错误的传播 网络,被独立地引导到被认为是相同的数学模型, 在统计力学中。首席研究员将尝试统一和扩展 这些模型的一些早期结果,通过使用最近的概率技术;一些 这涉及到与计算机科学家的合作。最近,新的方法 它的出现是为了利用底层网络几何结构中的对称性, 更好地理解随机过程;研究人员将开发和应用 这些方法进一步。最后,一个粒子的不规则随机运动的轨迹 被概率学家深入研究;这项研究将调查某些新的 试图解释它们的几何结构。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Yuval Peres其他文献
An isoperimetric inequality for the Wiener sausage
- DOI:
10.1007/s00039-012-0184-5 - 发表时间:
2012-08-01 - 期刊:
- 影响因子:2.500
- 作者:
Yuval Peres;Perla Sousi - 通讯作者:
Perla Sousi
Projections of the natural measure for percolation fractals
- DOI:
10.1007/s11856-016-1343-4 - 发表时间:
2016-09-07 - 期刊:
- 影响因子:0.800
- 作者:
Yuval Peres;Michał Rams - 通讯作者:
Michał Rams
Monotonicity of uniqueness for percolation on Cayley graphs: all infinite clusters are born simultaneously
- DOI:
10.1007/s004400050208 - 发表时间:
1999-02-01 - 期刊:
- 影响因子:1.600
- 作者:
Olle Häggström;Yuval Peres - 通讯作者:
Yuval Peres
A ug 2 01 7 MIXING TIME ESTIMATION IN REVERSIBLE MARKOV CHAINS FROM A SINGLE SAMPLE PATH
A ug 2 01 7 单样本路径的可逆马尔可夫链混合时间估计
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
Daniel J. Hsu;A. Kontorovich;D. A. Levin;Yuval Peres;Csaba Szepesvari - 通讯作者:
Csaba Szepesvari
Formation of an interface by competitive erosion
- DOI:
10.1007/s00440-016-0715-3 - 发表时间:
2016-05-10 - 期刊:
- 影响因子:1.600
- 作者:
Shirshendu Ganguly;Lionel Levine;Yuval Peres;James Propp - 通讯作者:
James Propp
Yuval Peres的其他文献
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{{ truncateString('Yuval Peres', 18)}}的其他基金
Invariant point processes, fair allocations, random-turn games and applications
不变点过程、公平分配、随机回合博弈及应用
- 批准号:
0605166 - 财政年份:2006
- 资助金额:
$ 8.67万 - 项目类别:
Continuing Grant
Collaborative Research FRG: Phase Transitions in Stochastics Dynamics and Algorithms
合作研究 FRG:随机动力学和算法中的相变
- 批准号:
0244479 - 财政年份:2003
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
Spin Systems on Graphs, Critical Percolation and Scaling Limits
图上的自旋系统、临界渗透和缩放限制
- 批准号:
0104073 - 财政年份:2001
- 资助金额:
$ 8.67万 - 项目类别:
Continuing Grant
Mathematical Sciences: "Percolation on Trees, Intersections of Random Sets, and Measures of Full Hausdorff Dimension"
数学科学:“树上的渗透、随机集的交集以及完整豪斯多夫维度的测量”
- 批准号:
9404391 - 财政年份:1994
- 资助金额:
$ 8.67万 - 项目类别:
Standard Grant
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