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Anita Kollwitz

Konstantin Recke, WWU: Percolation on Nonamenable Groups (Oberseminar Mathematische Stochastik)

Wednesday, 21.04.2021 17:00 per ZOOM: 61828242813

Mathematik und Informatik

In classical Bernoulli bond percolation (BBP) the edges of the graph \( Z^d\) are removed independently of each other and with a certain fixed probability $p \in [0,1]$. In this talk, we will discuss a generalized approach and some beautiful results due to Benjamini, Lyons, Peres and Schramm: The set-up is extended to locally finite connected infinite graphs and the probabilistic models are so-called ?invariant percolations?, i.e. random subgraphs whose laws are invariant under the action of some automorphism group of the underlying graph. Under suitable assumptions these models satisfy an equality known as the ?mass-transport principle?, which is extremely useful in analyzing existence and number of infinite connected components. We will mostly focus on the special case of Cayley graphs of nonamenable (finitely generated) groups, which are particularly interesting because BBP exhibits quite different behavior compared to the classical setting.



Angelegt am Monday, 12.04.2021 14:42 von Anita Kollwitz
Geändert am Wednesday, 21.04.2021 09:56 von Anita Kollwitz
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