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The KPZ equation and moments of random matrices
Vadim Gorinab, Sasha Sodincd 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.
DOI:
https://doi.org/10.15407/mag14.03.286
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MSC: 60B20, 60H15 Received: 29.01.2018
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Citation:
Vadim Gorin, Sasha Sodin, “The KPZ equation and moments of random matrices”, Zh. Mat. Fiz. Anal. Geom., 14:3 (2018), 286–296
Citation in format AMSBIB
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\by Vadim~Gorin, Sasha~Sodin
\paper The KPZ equation and moments of random matrices
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2018
\vol 14
\issue 3
\pages 286--296
\mathnet{http://mi.mathnet.ru/jmag701}
\crossref{https://doi.org/10.15407/mag14.03.286}
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http://mi.mathnet.ru/eng/jmag701 http://mi.mathnet.ru/eng/jmag/v14/i3/p286
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