Probability and Stochastic Analysis Seminar  RSS

19/06/2024, 17:00 — 18:00 — Online
Dieter Mitsche, Pontificia Universidad Católica de Chile

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

  1. the probability that the largest connected component is much smaller than expected;
  2. the size of the second-largest component;
  3. 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.

link

Except for a few of the oldest sessions these are from the Seminário de Probabilidade e Mecânica Estatística at IMPA which is co-sponsored by several institutions, in particular Instituto Superior Técnico.