117 citations · 544 across the 23 of their papers we have counts for
23 papers · 1 filter
The least singular value of the general deformed Ginibre ensemble
Mariya Shcherbina, Tatyana Shcherbina
We study the least singular value of the matrix with , where is drawn from the complex Ginibre ensemble of matrices with iid Gaussian entries, an…
Finite-rank complex deformations of random band matrices: sigma-model approximation
Mariya Shcherbina, Tatyana Shcherbina
We study the distribution of complex eigenvalues of random Hermitian block band matrices with a complex deformation of a finite rank. Assuming that th…
Universality for 1 d random band matrices
Mariya Shcherbina, Tatyana Shcherbina
We consider 1d random Hermitian block band matrices consisting of random Gaussian blocks (parametrized by , ) with a fi…
Transfer operator approach to 1d random band matrices
Mariya Shcherbina, Tatyana Shcherbina
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of character…
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…
Universality for 1d random band matrices: sigma-model approximation
Mariya Shcherbina, Tatyana Shcherbina
The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in J Stat Phys 164:1233 -- 1260, 2016; Commun Math P…
Transfer matrix approach to 1d random band matrices: density of states
Mariya Shcherbina, Tatyana Shcherbina
We study the special case of 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix . Ass…
Characteristic polynomials for 1D random band matrices from the localization side
Mariya Shcherbina, Tatyana Shcherbina
We study the special case of 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by . Assuming that…
On fluctuations of eigenvalues of random band matrices
Mariya Shcherbina
We consider the fluctuation of linear eigenvalue statistics of random band matrices whose entries have the form w…
Fluctuations of the eigenvalue number in the fixed interval for -models with
Mariya Shcherbina
We study the fluctuation of the eigenvalue number of any fixed interval inside the spectrum for - ensembles of random matrices in the case . We assume that th…
Change of variables as a method to study general -models: bulk universality
Mariya Shcherbina
We consider matrix models with real analytic potentials. Assuming that the corresponding equilibrium density has a one-interval support (without loss of generality $σ=[-2,2…
Fluctuations of linear eigenvalue statistics of matrix models in the multi-cut regime
Mariya Shcherbina
We study the asymptotic expansion in for the partition function of matrix models with real analytic potentials in the multi-cut regime up to the terms. As a res…
Quantum Hopfield Model
Masha Shcherbina, Brunello Tirozzi
We find the free-energy in the thermodynamic limit of a one dimensional XY model associated to a system of N qubits. The coupling among the sigma_i^z is a long range two bodies ran…
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Diluted regime
Maria Shcherbina, Brunello Tirozzi
We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide cla…
Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices
Mariya Shcherbina
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistic…
Orthogonal and symplectic matrix models: universality and other properties
M. Shcherbina
We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to…
Fluctuations of eigenvalues of matrix models and their applications
T. Kriecherbauer, M. Shcherbina
We study the expectation of linear eigenvalue statistics of matrix models with any , assuming that the potential is a real analytic function and that the corresponding equ…
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs
M. Shcherbina, B. Tirozzi
We consider the adjacency matrix of a large random graph and study fluctuations of the function with . W…
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…
On Universality for Orthogonal Ensembles of Random Matrices
M. Shcherbina
We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spe…
Stability of the dynamics of an asymmetric neural network
J. F. Feng, M. Shcherbina, B. Tirozzi
We study the stability of the dynamics of a network of n neurons intercting linearly through a random gaussian matrix of excitatory and inhibitory type. Using the aproach developed…
Dynamical behavior of a large complex system
J. F. Feng, M. Shcherbina, B. Tirozzi
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details an…
Rigorous Solution of the Gardner Problem
M. Shcherbina, B. Tirozzi
We prove rigorously the well-known result of Gardner about the typical fractional volume of interactions between N spins which solve the problem of storing a given set of random pa…