László Erdős

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We consider N×N symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure ν with a subexponential decay. We prove that the local eigenvalue statistics in the bulk of the spectrum for these matrices coincide with those of the Gaussian Orthogonal(More)
We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual A ∈ Lloc condition on the vector potential which does not allow to consider such singular fields. We extend Aharonov-Casher theorem for magnetic fields that(More)
The Pauli operator describes the energy of a nonrelativistic quantum particle with spin 1 2 in a magnetic field and an external potential. A new Lieb-Thirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first)(More)
Eugene Wigner’s revolutionary vision predicted that the energy levels of large complex quantum systems exhibit a universal behavior: the statistics of energy gaps depend only on the basic symmetry type of the model. These universal statistics show strong correlations in the form of level repulsion and they seem to represent a new paradigm of point processes(More)
Einstein’s kinetic theory of the Brownian motion, based upon light water molecules continuously bombarding a heavy pollen, provided an explanation of diffusion from the Newtonian mechanics. Since the discovery of quantum mechanics it has been a challenge to verify the emergence of diffusion from the Schrödinger equation. The first step in this program is to(More)
We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue −1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X∗X, where the variances of the entries of X(More)
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