Anita Kollwitz

Arne Grauer, Köln: Chemical distance in geometric random graphs with long edges and scale-free degree distribution (Oberseminar Mathematische Stochastik)

Wednesday, 04.05.2022 17:00 im Raum M4

Mathematik und Informatik

We study the occurence of ultrasmallness in geometric random graphs defined on the points of a Poisson process in d-dimensional space, which additionally carry independent random marks. In our framework, edges are established at random using the marks of the endpoints and the distance between points in a flexible way such that a large class of graph models with scale-free degree distribution and edges spanning large distances is included. We give a sharp criteria for the absence of ultrasmallness of the graphs and in the ultrasmall regime establish a limit theorem for the chemical distance of two points. Here, the boundary of the ultrasmall regime and the limit theorem depend not only on the power-law exponent of the graphs but also on a geometric quantity, the influence of the spatial distance of two typical points on the probability of an edge connecting them. The talk is based on joint work with Peter Gracar and Peter Mörters

Angelegt am Thursday, 31.03.2022 09:58 von Anita Kollwitz
Geändert am Thursday, 31.03.2022 15:08 von Anita Kollwitz
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