Rare events in sparse random graphs, random trees and coagulation processes

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In this talk, we would like to give an overview on recent and past results on large deviations for sparse random graphs and coagulation processes. In particular, recently there have been progresses in the study of inhomogeneous random graphs and random graphs with marks in this framework, with some interesting similarities between different models appear when studying their large deviation rate functions. On the other hand, an approach that exploits the description of interaction in spatial coagulation processes with random tree-like structures has proved useful in proving large deviations for such Markov processes. We will describe such approach and outline possible future directions.

This talk is based on joint works with W. K ̈onig, H. Langhammer, E. Magnanini (WIAS Berlin) and M. Kolodziejczyk (PoliMi).

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