LDP for graphons
We discuss the large deviation theory in the context of a sequence of measures on the graphon space that is obtained by sampling from a fixed graphon. In the case of constant graphons, the existence of LDP with speed $n^2$ was proved by Chatterjee and Varadhan and it was then used to investigate the upper tail problem of triangle counts for homogeneous Erdős–Rényi random graph. In this talk, we show that sampling from a general graphon may lead to two non-trivial LDPs that correspond to speed $n$ and $n^2$.
This is a joint work with O.Pikhurko.