Percolation in the Poisson Boolean model

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This talk will be broadcast at 13:30 BST November 27th 2024 on MS Teams only.

Meeting ID: 393 527 089 878
Passcode: dsm7py

Abstract

My talk will focus on the Poisson-Bolean model with convex grains. This model is constructed from a homogeneous Poisson point process in space with positive intensity u. At each point of this process we attach an iid copy of a random convex body. To characterize these convex bodies, we introduce a sequence of decreasing diameters. I will start with an introduction to the model and explain how the diameters are derived. I will give several criteria for the distribution of the diameters and moment conditions on the volume of the convex body that lead to different behaviors of the model. We observe complete covering of the space by the convex bodies, the existence of an unbounded connected component of the convex bodies as long as u is positive or no unbounded connected component if u is positive but sufficiently small. Importantly, our results contain no restrictions on the joint distribution of the diameters. This work is based on joint work with Peter Gracar and Peter Mörters.

About Marilyn

Marilyn is a PhD Student at the University of Cologne under the supervision of Prof. Peter Mörters. Her main area of interest is probability theory with a focus on random graphs and percolation theory.