Professor László Erdős

Research Priorities: Probability theory, random matrices, mathematical physics, complex quantum systems
László Erdős is a Hungarian-German mathematician. He works on the mathematical basis of the groundbreaking vision of the Hungarian-American physicist and Nobel Prize Winner Eugene Paul Wigner, according to which large complex quantum systems have universal properties that correspond to the spectrum of large random matrices. He also investigates magnetic Lieb-Thirring inequalities, Brownian motion in the classic and quantum mechanical case, the Gross-Pitaveskii equation for Bose-Einstein condensate, and the derivation of kinetic equations such as the Boltzmann equation from quantum mechanics. His work is essential to the understanding of physical phenomena.
As a mathematical physicist, László Erdős’s research focuses on mathematically rigorous results, which are inspired in particular by quantum physics. His most important research results include the derivation of the linear Boltzmann equation and quantum diffusion from the Schroedinger equation with weak random potential, as well as the proof of the validity of the time-dependent Gross-Pitaevskii equation from interactive multi-particle dynamism. These results make it possible to substitute the physically fundamental but mathematically impractical equations in very high dimensions with simpler, effective equations in much lower dimensions.
László Erdős also studies the theory of random matrices, originally motivated by the groundbreaking vision of Eugene Wigner, which predicts that eigenvalue statistics of a hermetic random matrix follow a universal pattern. The aim is to prove the universality of this famous Wigner-Dyson-Mehta statistic in various important matrix models. For fifty years, this question was an assumption concerning the simplest case of Wigner matrices, and was then solved by László Erdős (working together with the Taiwanese-American mathematician Horng-Tzer Yau and the Italian-American mathematician Benjamin Schlein) using new methods based on Dyson-Brownian motion. László Erdős has since expanded this theory to far more general models with correlations and inhomogeneities. His newest findings focus on non-hermetic random matrices, the spectrum of which is far more complex.
László Erdős’s research results provide mathematical tools for researchers in statistics, data science, neuroscience, and quantum computing. They make it possible to reliably predict the properties of large quantum systems, to create algorithms for complex data sets, and to develop robust models for unbalanced processes in technology and the natural sciences.