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 …

Suppose that X is a bounded-degree polynomial with nonnegative coefficients on the p-
biased discrete hypercube. Our main result gives sharp estimates on the logarithmic upper …

We establish precise estimates for the probability of rare events of the largest eigenvalue of
Wigner matrices with sub-Gaussian entries. In contrast to the case of Wigner matrices with …

Let $\Xi $ be the adjacency matrix of an Erd\H {o} sR\'enyi graph on $ n $ vertices and with
parameter $ p $ and consider $ A $ a $ n\times n $ centered random symmetric matrix with …

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 …

In this note, we study large deviations of the number NN of intercalates (2× 2 2*2
combinatorial subsquares which are themselves Latin squares) in a random n× nn*\,n Latin …

The upper tail problem for the largest eigenvalue of the Erdös--Rényi random graph G_n,p
is to estimate the probability that the largest eigenvalue of the adjacency matrix of G_n,p …

Consider a random symmetric matrix with iid~ entries on and above its diagonal that are
products of Bernoulli random variables and random variables with sub-Gaussian tails. Such …

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 …

The upper tail problem in a random graph asks to estimate the probability that the number of
copies of some fixed subgraph in an Erdős‐Rényi random graph exceeds its expectation by …