---
_id: '1507'
abstract:
- lang: eng
text: 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.
acknowledgement: The author is partially supported by SFB-TR 12 Grant of the German
Research Council.
article_processing_charge: No
author:
- first_name: László
full_name: Erdös, László
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
citation:
ama: 'Erdös L. Random matrices, log-gases and Hölder regularity. In: *Proceedings
of the International Congress of Mathematicians*. Vol 3. International Congress
of Mathematicians; 2014:214-236.'
apa: 'Erdös, L. (2014). Random matrices, log-gases and Hölder regularity. In *Proceedings
of the International Congress of Mathematicians* (Vol. 3, pp. 214–236). Seoul,
Korea: International Congress of Mathematicians.'
chicago: Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” In *Proceedings
of the International Congress of Mathematicians*, 3:214–36. International Congress
of Mathematicians, 2014.
ieee: L. Erdös, “Random matrices, log-gases and Hölder regularity,” in *Proceedings
of the International Congress of Mathematicians*, Seoul, Korea, 2014, vol.
3, pp. 214–236.
ista: '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.'
mla: Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” *Proceedings
of the International Congress of Mathematicians*, vol. 3, International Congress
of Mathematicians, 2014, pp. 214–36.
short: L. Erdös, in:, Proceedings of the International Congress of Mathematicians,
International Congress of Mathematicians, 2014, pp. 214–236.
conference:
end_date: 2014-08-21
location: Seoul, Korea
name: 'ICM: International Congress of Mathematicians'
start_date: 2014-08-13
date_created: 2018-12-11T11:52:25Z
date_published: 2014-08-01T00:00:00Z
date_updated: 2023-10-17T11:12:55Z
day: '01'
department:
- _id: LaEr
ec_funded: 1
intvolume: ' 3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1407.5752
month: '08'
oa: 1
oa_version: Submitted Version
page: 214 - 236
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '338804'
name: Random matrices, universality and disordered quantum systems
publication: Proceedings of the International Congress of Mathematicians
publication_status: published
publisher: International Congress of Mathematicians
publist_id: '5670'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Random matrices, log-gases and Hölder regularity
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2014'
...