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Titlebook: Coarse Geometry and Randomness; école d’été de Proba Itai Benjamini Book 2013 Springer International Publishing Switzerland 2013 82B43,82B4

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樓主
發(fā)表于 2025-3-21 18:38:48 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Coarse Geometry and Randomness
副標(biāo)題école d’été de Proba
編輯Itai Benjamini
視頻videohttp://file.papertrans.cn/229/228715/228715.mp4
概述Includes many exercises of varying difficulty levels.Investigates many open problems.Presents topics not covered by any other book.Includes supplementary material:
叢書(shū)名稱Lecture Notes in Mathematics
圖書(shū)封面Titlebook: Coarse Geometry and Randomness; école d’été de Proba Itai Benjamini Book 2013 Springer International Publishing Switzerland 2013 82B43,82B4
描述.These lecture notes study the interplay between randomness and geometry of graphs. The first part of the notes reviews several basic geometric concepts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk..The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes is to point to some random metric spaces modeled by graphs that turn out to be somewhat exotic, that is, they admit a combination of properties not encountered in the vertex transitive world. These include percolation clusters on vertex transitive graphs, critical clusters, local and scaling limits of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ)..
出版日期Book 2013
關(guān)鍵詞82B43,82B41,05C81,05C10,05C80; Coarse geometry; Graphs; Percolation; Random walk; Unimodular random graph
版次1
doihttps://doi.org/10.1007/978-3-319-02576-6
isbn_softcover978-3-319-02575-9
isbn_ebook978-3-319-02576-6Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer International Publishing Switzerland 2013
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 23:08:32 | 只看該作者
Book 2013ts, before moving on to examine the manifestation of the underlying geometry in the behavior of random processes, mostly percolation and random walk..The study of the geometry of infinite vertex transitive graphs, and of Cayley graphs in particular, is fairly well developed. One goal of these notes
板凳
發(fā)表于 2025-3-22 01:36:04 | 只看該作者
Percolation Perturbations,emerge. When the clusters are subcritical, we see random perturbation of the underling graphs but when the construction is based on critical percolation new type of spaces emerges. More precise definitions appears below. We end with an invariant percolation viewpoint on the incipient infinite cluster (IIC).
地板
發(fā)表于 2025-3-22 06:43:35 | 只看該作者
5#
發(fā)表于 2025-3-22 09:41:12 | 只看該作者
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發(fā)表于 2025-3-22 16:05:24 | 只看該作者
Book 2013of graphs, long range percolation, CCCP graphs obtained by contracting percolation clusters on graphs, and stationary random graphs, including the uniform infinite planar triangulation (UIPT) and the stochastic hyperbolic planar quadrangulation (SHIQ)..
7#
發(fā)表于 2025-3-22 20:00:31 | 只看該作者
8#
發(fā)表于 2025-3-23 00:51:54 | 只看該作者
Local Limits of Graphs,ous sections. If . = (., .) is such a graph, and ., . ∈ ., the graph distance between . and . in . is defined to be the length of a shortest path in . between . and ., and is denoted by ..(., .). A . graph (., .) is a graph . together with a distinguished vertex . of ..
9#
發(fā)表于 2025-3-23 03:09:07 | 只看該作者
Uniqueness of the Infinite Percolation Cluster,wer to this question leads to a rather rich landscape with applications in group theory and many still open problems. In this section we study the question of the number of infinite clusters in percolation configurations in the regime . > ...
10#
發(fā)表于 2025-3-23 08:14:30 | 只看該作者
Percolation Perturbations,sters in the non uniqueness regime on the other hand admit some universal features which are not inherited from the underling graph, they have infinitely many ends and thus are very tree like. When performing the operation of contracting Bernoulli percolation clusters different geometric structures
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