Vadim Gorin, Sasha Sodin, “The KPZ equation and moments of random matrices”, Zh. Mat. Fiz. Anal. Geom., 2018, Volume 14, Number 3,Pages <nobr>286–296</nobr>

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JOURNALS // Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry] // Archive

Zh. Mat. Fiz. Anal. Geom., 2018 Volume 14, Number 3, Pages 286–296 (Mi jmag701)

This article is cited in 3 papers

The KPZ equation and moments of random matrices

Vadim Gorin^ab, Sasha Sodin^cd

^a Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA
^b Institute for Information Transmission Problems of Russian Academy of Sciences, Bolshoy Karetny per. 19, build. 1, Moscow 127051, Russia
^c School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel
^d School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom

Abstract: The logarithm of the diagonal matrix element of a high power of a random matrix converges to the Cole–Hopf solution of the Kardar–Parisi–Zhang equation in the sense of one-point distributions.

Key words and phrases: KPZ equation, Cole–Hopf solution, Airy process, random matrices.

MSC: 60B20, 60H15

Received: 29.01.2018

Language: English

DOI: 10.15407/mag14.03.286

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© Steklov Math. Inst. of RAS, 2025