Journal of Mathematical Physics, Analysis, Geometry
2018, vol. 14, No 3, pp. 286-296     ( to contents , go back )

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

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

Received January 29, 2018.

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


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.

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