274 citations · 957 across the 29 of their papers we have counts for
11 papers · 1 filter
On Random Matrices Arising in Deep Neural Networks. Gaussian Case
Leonid Pastur
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the…
How much delocalisation is needed for an enhanced area law of the entanglement entropy?
Peter Müller, Leonid Pastur, Ruth Schulte
We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logari…
Szegö-type Theorems for One-Dimensional Schrodinger Operator with Random Potential (smooth case)
L. Pastur, M. Shcherbina
The paper is a continuation of work [15] in which the general setting for analogs of the Szegö theorem for ergodic operators was given and several interesting cases were considered…
On a Limiting Distribution of Singular Values of Random Band Matrices
Anna Lytova, Leonid Pastur
An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and ran…
On a Random Matrix Models of Quantum Relaxation
J. L. Lebowitz, A. Lytova, L. Pastur
Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a reservoir and assuming that the interaction is modelled by a rando…
Bulk Universality and Related Properties of Hermitian Matrix Models
L. Pastur, M. Shcherbina
We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally and…