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- László Erdős
- 2009

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)

- László Erdős, Vitali Vougalter
- 2001

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)

- László Erdős, Jan Philip Solovej
- 2003

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)

- László Erdős
- 2003

The Pauli operator describes the energy of a nonrelativistic quantum particle with spin 12 in a magnetic field and an external potential. Bounds on the sum of the negative eigenvalues are called magnetic Lieb-Thirring (MLT) inequalities. The purpose of this paper is twofold. First, we prove a new MLT inequality in a simple way. Second, we give a short… (More)

- László Erdős
- 2006

We present a review on the recent developments concerning rigorous mathematical results on Schrödinger operators with magnetic fields. This paper is dedicated to the sixtieth birthday of Barry Simon. AMS 2000 Subject Classification 81Q10, 81Q70 Running title: Recent developments on magnetic fields

- László Erdős
- 2013

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)

- László Erdős
- 2010

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)

- Oskari Ajanki, László Erdős, Torben Krüger
- Journal of statistical physics
- 2016

We prove optimal local law, bulk universality and non-trivial decay for the off-diagonal elements of the resolvent for a class of translation invariant Gaussian random matrix ensembles with correlated entries.

- László Erdős
- 2017

These lecture notes are a concise introduction of recent techniques to prove local spectral universality for a large class of random matrices. The general strategy is presented following the recent book with H.T. Yau [43]. We extend the scope of this book by focusing on new techniques developed to deal with generalizations of Wigner matrices that allow for… (More)

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