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The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev-Petviashvili (KP) equation.
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Mark. Ablowitz and Harvey Segur · 1979
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V.. Zaharov and A.. Sabat · 1979
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B.. Konopelchenko · 1982
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“The Fredholm determinant method for the KdV equations”
Christoph P\"oppe · 1984
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“Dynamical scaling of growing interfaces”
M. Kardar, G. Parisi and Y.-C. Zhang · 1986
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“Fredholm determinants and the τ \tau function for the Kadomtsev-Petviashvili hierarchy”
Ch. P\"oppe and D.. Sattinger · 1988
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“General determinants and the τ \tau function for the Kadomtsev-Petviashvili hierarchy”
Christoph P\"oppe · 1989
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“Level-spacing distributions and the Airy kernel”
Craig. Tracy and Harold Widom · 1994
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“On orthogonal and symplectic matrix ensembles”
Craig. Tracy and Harold Widom · 1996
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“Global solutions for the KdV equation with unbounded data”
Carlos. Kenig, Gustavo Ponce and Luis Vega · 1997
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“Shape fluctuations and random matrices”
Kurt Johansson · 2000
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“Solitons” Differential equations, symmetries and infinite-dimensional algebras, Translated from the 1993 Japanese original by Miles Reid 135
T. Miwa, M. Jimbo and E. Date · 2000
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“Discrete polynuclear growth and determinantal processes”
Kurt Johansson · 2003
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“Matrix Kadomtsev-Petviashvili equation: matrix identities and explicit non-singular solutions”
A Sakhnovich · 2003
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“A system of differential equations for the Airy process”
Craig. Tracy and Harold Widom · 2003
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“PDEs for the joint distributions of the Dyson, Airy and sine processes”
Mark Adler and Pierre van Moerbeke · 2005
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“Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices”
Jinho Baik, G\’erard Ben and Sandrine P\’ech\’e · 2005
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Tomohiro Sasamoto · 2005
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“Fredholm determinants”
Henry. McKean · 2011
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“Exact Solution for the Stationary Kardar-Parisi-Zhang Equation”
Takashi Imamura and Tomohiro Sasamoto · 2012
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“The KPZ equation with flat initial condition and the directed polymer with one free end”
Pierre Le and Pasquale Calabrese · 2012
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“Stationary correlations for the 1D KPZ equation”
Takashi Imamura and Tomohiro Sasamoto · 2013
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“Free energy fluctuations for directed polymers in random media in 1 + 1 1+1 dimension”
Alexei Borodin, Ivan Corwin and Patrik Ferrari · 2014
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