Luisa Andreis, Dipartimento di Matematica, Politecnico di Milano.

Rare events for dense random graphs are well described using the theory of large deviations and graphons. When graphs are sparse the picture is less clear, objects that describe globally the graphs and their limits, as graphons do for dense graphs, have not been defined yet. Nevertheless we do have information on how these graphs look like when explored locally from a vertex and this, under some assumptions, gives also information on global properties. In this talk we will give an overview on what is known on rare events in this regime, focusing in particular on large deviation statements on connected components in inhomogeneous random graphs and on links with coagulation processes.

This talk is based on joint works with Wolfgang K¨onig (WIAS and TU Berlin),
Tejas Iyer, Heide Langhammer, Elena Magnanini and Robert Patterson (WIAS).