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19/06/2024, 17:00 — 18:00 — Online

Dieter Mitsche, *Pontificia Universidad Católica de Chile*

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Component sizes in spatial random graphs

We consider a large class of supercritical spatially embedded random graphs, including among others long-range percolation and geometric inhomogeneous random graphs, and identify a single exponent zeta depending on the model parameters that describes the asymptotics of

- the probability that the largest connected component is much smaller than expected;
- the size of the second-largest component;
- the distribution of the size of the component containing a distinguished vertex.

In the talk, I will explain the relation between the three quantities and give some intuition for the values of zeta in different regimes.

Joint work with Joost Jorritsma and Júlia Komjáthy.