Addendum
发表于 2025-3-21 18:38:48
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农学
发表于 2025-3-21 23:08:32
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
Nausea
发表于 2025-3-22 01:36:04
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).
Priapism
发表于 2025-3-22 06:43:35
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grudging
发表于 2025-3-22 09:41:12
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刚毅
发表于 2025-3-22 16:05:24
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)..
刚毅
发表于 2025-3-22 20:00:31
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BOOST
发表于 2025-3-23 00:51:54
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 ..
d-limonene
发表于 2025-3-23 03:09:07
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 . > ...
禁令
发表于 2025-3-23 08:14:30
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