Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 3, pp. 286-296   https://doi.org/10.15407/mag14.03.286     ( to contents , go back )
https://doi.org/10.15407/mag14.03.286

The KPZ Equation and Moments of Random Matrices

Vadim Gorin

Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA,
Institute for Information Transmission Problems of Russian Academy of Sciences, Bolshoy Karetny per. 19, build. 1, Moscow 127051, Russia
E-mail: vadicgor@gmail.com

Sasha Sodin

School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom,
School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel
E-mail: a.sodin@qmul.ac.uk

Received January 29, 2018.

Dedicated to V.A. Marchenko on his 95-th birthday

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.

Mathematics Subject Classification 2000: 60B20, 60H15.
Key words: KPZ equation, Cole–Hopf solution, Airy process, random matrices.

Download 339834 byte View Contents