Spectral Edge in Sparse Random Graphs: Upper and Lower Tail Large Deviations

Bhaswar B. Bhattacharya, Sohom Bhattacharya, Shirshendu Ganguly

In this paper we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erdős-Rényi random graph ${\mathcal{G}}_{n,p}$, in t…