Cluster sizes in subcritical soft Boolean models (Lukas Lüchtrath, Berlin)

02.12.2024 16:15 – 18:00

Abstract:
In this talk, we consider the soft Boolean model, a model that interpolates between two standard models of percolation: the classical Boolean model (viewed as a graph) and long-range percolation. Specifically, the model incorporates a heavy-tailed degree distribution and long-range edges. We study the subcritical one-arm probability and determine its tail behaviour. To this end, we explain how a path connecting the origin to a far distance relies on an interplay between the heavy-tailed degrees and the long-range edges. Furthermore, we compare the result with the tail probability of the number of vertices in a typical cluster, which depends on the degree-distribution alone. The proofs rest on a fine path-counting method, which we present in greater detail. The talk is based on joint work with Benedikt Jahnel and Marcel Ortgiese.

Lieu

Conseil Général 7-9, Room 1-15, Séminaire Math Physics

entrée libre