Gumbel central limit theorem for max-min and min-max

  • The max-min and min-max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the max-min and min-max is challenging as matrices are large and full information about their entries is lacking. Here we take a statistical-physics approach and establish limit laws—akin to the central limit theorem—for the max-min and min-max of large random matrices. The limit laws intertwine random-matrix theory and extreme-value theory, couple the matrix dimensions geometrically, and assert that Gumbel statistics emerge irrespective of the matrix entries' distribution. Due to their generality and universality, as well as their practicality, these results are expected to have a host of applications in the physical sciences and beyond.

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Author:Iddo EliazarORCiD, Ralf MetzlerORCiDGND, Shlomi ReuveniORCiD
Pubmed Id:
Parent Title (English):Physical review : E, Statistical, nonlinear and soft matter physics
Publisher:American Physical Society
Place of publication:College Park
Document Type:Article
Year of first Publication:2019
Year of Completion:2019
Release Date:2020/11/20
Page Number:6
Funder:Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [ME 1535/7-1]; Foundation for Polish Science within an Alexander von Humboldt Polish Honorary Research Scholarship; Azrieli Foundation; Sackler Center for Computational Molecular and Materials Science
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Publication Way:Open Access
Open Access / Green Open-Access