The evolution of a deep neural network trained by the gradient descent in the
overparametrization regime can be described by its neural tangent kernel (NTK)\cite {jacot2018neural, …

We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of
random matrices that includes the normalized adjacency matrices of the Erd{\H o}sR{\'e}nyi …

In this paper, we compare the solutions of the Dyson Brownian motion for general $$\beta $$
β and potential V and the associated McKean–Vlasov equation near the edge. Under …

Numerous deep learning algorithms have been inspired by and understood via the notion of
information bottleneck, where unnecessary information is (often implicitly) minimized while …

In this paper we show that a Brownian Gibbsian line ensemble whose top curve approximates
a parabola must be given by the parabolic Airy line ensemble. More specifically, we prove …

Score-based generative models have emerged as a powerful approach for sampling high-dimensional
probability distributions. Despite their effectiveness, their theoretical …

Consider the normalized adjacency matrices of random $d$-regular graphs on $N$ vertices
with fixed degree $d\geq 3$, and denote the eigenvalues as $\lambda_1=d/\sqrt{d-1}\geq \…

We study uniformly random lozenge tilings of general simply connected polygons. Under a
technical assumption that is presumably generic with respect to polygon shapes, we show …

The Airy$_\beta$ line ensemble is an infinite sequence of random curves. It is a natural
extension of the Tracy-Widom$_\beta$ distributions, and is expected to be the universal edge …

We study the adjacency matrices of random d-regular graphs with large but fixed degree d.
In the bulk of the spectrum $${[-2\sqrt{d-1}+\varepsilon, 2\sqrt{d-1}-\varepsilon]}$$ [ - 2 d - 1 + …