conference paper
Random matrices, log-gases and Hölder regularity
published
yes
László
Erdös
author 4DBD5372-F248-11E8-B48F-1D18A9856A870000-0001-5366-9603
LaEr
department
ICM: International Congress of Mathematicians
Random matrices, universality and disordered quantum systems
project
The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large real and complex Hermitian matrices with independent, identically distributed entries are universal in a sense that they depend only on the symmetry class of the matrix and otherwise are independent of the details of the distribution. We present the recent solution to this half-century old conjecture. We explain how stochastic tools, such as the Dyson Brownian motion, and PDE ideas, such as De Giorgi-Nash-Moser regularity theory, were combined in the solution. We also show related results for log-gases that represent a universal model for strongly correlated systems. Finally, in the spirit of Wigner’s original vision, we discuss the extensions of these universality results to more realistic physical systems such as random band matrices.
International Congress of Mathematicians2014Seoul, Korea
eng
Proceedings of the International Congress of Mathematicians
3214 - 236
Erdös, L. (2014). Random matrices, log-gases and Hölder regularity. In <i>Proceedings of the International Congress of Mathematicians</i> (Vol. 3, pp. 214–236). Seoul, Korea: International Congress of Mathematicians.
Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” In <i>Proceedings of the International Congress of Mathematicians</i>, 3:214–36. International Congress of Mathematicians, 2014.
Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” <i>Proceedings of the International Congress of Mathematicians</i>, vol. 3, International Congress of Mathematicians, 2014, pp. 214–36.
Erdös L. Random matrices, log-gases and Hölder regularity. In: <i>Proceedings of the International Congress of Mathematicians</i>. Vol 3. International Congress of Mathematicians; 2014:214-236.
L. Erdös, in:, Proceedings of the International Congress of Mathematicians, International Congress of Mathematicians, 2014, pp. 214–236.
Erdös L. 2014. Random matrices, log-gases and Hölder regularity. Proceedings of the International Congress of Mathematicians. ICM: International Congress of Mathematicians vol. 3, 214–236.
L. Erdös, “Random matrices, log-gases and Hölder regularity,” in <i>Proceedings of the International Congress of Mathematicians</i>, Seoul, Korea, 2014, vol. 3, pp. 214–236.
15072018-12-11T11:52:25Z2023-10-17T11:12:55Z