IS11: Long range percolation models

date: 7/14/2025, time: 16:00-17:30, room: ICS 25

Organizer: Alexander Drewitz (Universität zu Köln)

Chair: Alexander Drewitz (Universität zu Köln)

Locality of long range percolation on groups of polynomial growth

Júlia Komjáthy (Delft University of Technology)

In this talk, we study long range percolation on vertex transitive graphs of polynomial growth converging locally in the Benjamini Schramm sense to the limiting graph G of dimension d. We assume the weak decay regime, when the (limiting) connectivity kernel decays as a polynomial of the graph distance with a power that is between d and 2d. Under natural conditions on the n-dependent kernels, we prove that the critical value of long range percolation (often denoted by beta_c) of G_n is converging to the that on the limiting graph. Joint work with Yago Moreno Alonzo.

Hausdorff dimension of the critical clusters for the metric graph Gaussian free field

Alexis Prévost (University of Bonn)

I will review recent results concerning the phase transition for a strongly correlated percolation model called the metric graph Gaussian free field. In particular, I will focus on the Hausdorff dimension of the critical connected components, as well as on the critical exponents which describe the volume of these components on graphs of intermediate dimension.

Indistinguishability of unbounded occupied and vacant components in Boolean models

Artem Sapozhnikov (Leipzig University)

We consider general Boolean models on Riemannian symmetric spaces driven by insertion or deletion tolerant point processes. For insertion (resp. deletion) tolerant Boolean models, we show that unbounded occupied (resp. vacant) connected components are indistinguishable by isometries invariant component properties. In particular, this implies the uniqueness monotonicity for both occupied and vacant sets of Poisson-Boolean models. This is a joint work with Yingxin Mu (Leipzig).