We study the fluctuations of the largest eigenvalue λ max of N× N random matrices in the
limit of large N. The main focus is on Gaussian β ensembles, including in particular the …

A bstract We show that in a general\(\mathcal {N}={1}\) supergravity with N≫ 1 scalar fields,
an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking …

In this paper, we compute two important information-theoretic quantities which arise in the
application of multiple-input multiple-output (MIMO) antenna wireless communication …

Classical neural networks with random initialization famously behave as Gaussian
processes in the limit of many neurons, which allows one to completely characterize their …

We study the probability distribution of the index N+, ie, the number of positive eigenvalues
of an N× N Gaussian random matrix. We show analytically that, for large N and large N+ with …

We consider a planar Coulomb gas ensemble of size $ N $ with the inverse temperature
$\beta= 2$ and external potential $ Q (z)=| z|^ 2-2c\log| za| $, where $ c> 0$ and …

We introduce a random matrix model for the stationary covariance of multivariate Ornstein-
Uhlenbeck processes with heterogeneous temperatures, where the covariance is …

The largest eigenvalue distribution of the Wishart–Laguerre ensemble, indexed by Dyson
parameter and Laguerre parameter a, is fundamental in multivariate statistics and finds …

Using the replica method, we compute analytically the average largest eigenvalue of diluted
covariance matrices of the form $\mathbf {J}=\mathbf {X}^ T\mathbf {X} $, where $\mathbf {X} …

We analyze statistical features of the'optimization landscape'in a random version of one of
the simplest constrained optimization problems of the least-square type: finding the best …