Thursday, January 18, 2024 - 16:00 in U2-135
Spatial Monotonicity Properties of Bernoulli Percolation
A talk in the Oberseminar Wahrscheinlichkeitstheorie series by
Thomas Richthammer from University Paderborn
| Abstract: |
We consider Bernoulli percolation on a graph $G = (V,E)$. Interpreting some chosen reference vertex o in V as the origin of an infection, the percolation cluster of o corresponds to the set of all infected vertices. It is very natural to expect that the probability for a vertex v in V to be infected should (in some sense) be decreasing in the distance of v to o. One possible rigorous formulation of this property is the famous bunkbed conjecture, which dates back to the 80s and still remains wide open. It seems that this kind of spatial monotonicity property of percolation in general is difficult to obtain. Here we present several new results relying on symmetry considerations or a Markov chain approach. Some of these results are joint work with Philipp König.
Within the CRC this talk is associated to the project(s): B10 |
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