peer reviewedWe derive a system of stochastic partial differential equations satisfied by the eigenvalues of the symmetric matrix whose entries are the Brownian sheets. We prove that the sequence Ld(s,t),(s,t)∈[0,S]×[0,T]d∈N of empirical spectral measures of the rescaled matrices is tight on C([0,S]×[0,T],P(R)) and hence is convergent as d goes to infinity by Wigner's semicircle law. We also obtain PDEs which are satisfied by the high-dimensional limiting measure
Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flo...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
AbstractLet {vij} i,j = 1, 2,…, be i.i.d. standardized random variables. For each n, let Vn = (vij) ...
peer reviewedWe derive a system of stochastic partial differential equations satisfied by the eigenv...
peer reviewedSince the introduction of Dyson's Brownian motion in early 1960s, there have been a lot...
AbstractConsider N×N Hermitian or symmetric random matrices H with independent entries, where the di...
peer reviewedIn this article, we obtain an equation for the high-dimensional limit measure of eigenv...
The probabilistic properties of eigenvalues of random matrices whose dimension increases indefinitel...
The free multiplicative Brownian motion $b_{t}$ is the large-$N$ limit of the Brownian motion on $\m...
AbstractLet Wn be n×n Hermitian whose entries on and above the diagonal are independent complex rand...
International audienceThis paper presents a novel approach to characterize the dynamics of the limit...
We define a new diffusive matrix model converging towards the β -Dyson Brownian motion for all β ∈ [...
In this thesis we examine the properties of Wigner matrices. We will give proofs for two fundamental...
In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample c...
This paper presents a novel approach to characterize the dynamics of the limit spectrum of large ran...
Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flo...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
AbstractLet {vij} i,j = 1, 2,…, be i.i.d. standardized random variables. For each n, let Vn = (vij) ...
peer reviewedWe derive a system of stochastic partial differential equations satisfied by the eigenv...
peer reviewedSince the introduction of Dyson's Brownian motion in early 1960s, there have been a lot...
AbstractConsider N×N Hermitian or symmetric random matrices H with independent entries, where the di...
peer reviewedIn this article, we obtain an equation for the high-dimensional limit measure of eigenv...
The probabilistic properties of eigenvalues of random matrices whose dimension increases indefinitel...
The free multiplicative Brownian motion $b_{t}$ is the large-$N$ limit of the Brownian motion on $\m...
AbstractLet Wn be n×n Hermitian whose entries on and above the diagonal are independent complex rand...
International audienceThis paper presents a novel approach to characterize the dynamics of the limit...
We define a new diffusive matrix model converging towards the β -Dyson Brownian motion for all β ∈ [...
In this thesis we examine the properties of Wigner matrices. We will give proofs for two fundamental...
In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample c...
This paper presents a novel approach to characterize the dynamics of the limit spectrum of large ran...
Consider the Dyson Brownian motion with parameter β, where β=1,2,4 corresponds to the eigenvalue flo...
We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with ce...
AbstractLet {vij} i,j = 1, 2,…, be i.i.d. standardized random variables. For each n, let Vn = (vij) ...
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