For any fixed simple graph H=(V, E) and any fixed u> 0, we establish the leading order of the
exponential rate function for the probability that the number of copies of H in the Erdős …

We establish precise upper-tail asymptotics and large deviation principles for the rightmost
eigenvalue $\lambda_1 $ of Wigner matrices with sub-Gaussian entries. In contrast to the …

We establish large deviation principles for the largest eigenvalue of large random matrices
with variance profiles. For $ N\in\mathbb N $, we consider random $ N\times N $ symmetric …

We show that for an Erd\H {o} sR\'{e} nyi graph on $ N $ vertices with expected degree $ d $
satisfying $\log^{-1/9} N\leq d\leq\log^{1/40} N $, the largest eigenvalues can be precisely …

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 G n, p, in the regime of …

For a‐regular connected graph H the problem of determining the upper tail large deviation
for the number of copies of H in, an Erdős‐Rényi graph on n vertices with edge probability p …

Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly
important subclass of such random matrices, useful in many applications, are what are …

We develop a quantitative large deviations theory for random hypergraphs, which rests on
tensor decomposition and counting lemmas under a novel family of cut-type norms. As our …

In this article we consider Wigner matrices (XN) N∈ N with variance profiles which are of the
form XN (i, j)= σ (i∕ N, j∕ N) ai, j∕ N where σ is a symmetric real positive function of [0, 1] 2 …

Large deviation behavior of the largest eigenvalue λ 1 of Wigner matrices including those
arising from an Erdős-Rényi random graph G n, p with iid random conductances on the …