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We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions.
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J. Baik and E.M. Rains, Symmetrized random permutations , Random Matrix Models and Their Applications, vol. 40, Cambridge University Press, 2001, pp. 1–19
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E. Katzav and M. Schwartz, Numerical evidence for stretched exponential relaxation in the Kardar-Parisi-Zhang equation , Phys. Rev. E 69
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M. Birkner, A condition for weak disorder for directed polymers in a random medium , El. Comm. Prob. 9
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2005
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K. Takeuchi and M. Sano, Growing interfaces of liquid crystal turbulence: universal scaling and fluctuations , Phys. Rev. Lett. 104
2010
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H. Lacoin, New bounds for the free energy of directed polymers in dimension 1+1 and 1+2 , Comm. Math. Phys. 294
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F. den Hollander, A key large deviation principle for interacting stochastic systems , Proceedings ICM 2010, Hyderabad, August 2010
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L. Canet, H. Chat, B. Delamotte, and N. Wschebor Nonperturbative renormalization group for the Kardar-Parisi-Zhang equation , Phys. Rev. Lett. 104
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G.W. Anderson, A. Guionnet, and O. Zeitouni, An Introduction to Random Matrices , Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2010
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S.C. Ferreira and S.G. Alves, Pitfalls on the determination of the universality class of radial clusters , J. Stat. Mech. (2006), P11007
2006
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C. Monthus and T. Garel, Freezing transition of the directed polymer in a 1 + d 1+d random medium: location of the critical temperature and unusual critical properties , Phys. Rev. E 74
2006
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H. C. Fogedby, Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension , Phys. Rev. E 73
2006
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H. Spohn, Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals , Physica A 369
2006
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M. Degawa, J.T. Stasevich, W.G. Cullen, A. Pimpinelli, T.L. Einstein and E.D. Williams, Distinctive fluctuations in a confined geometry , Phys. Rev. Lett. 97
2006
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M. Kardar, Statistical Mechanics of Fields , Cambridge University Press, 2007
2007
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A. Borodin, P.L. Ferrari, M. Prähofer, and T. Sasamoto, Fluctuation properties of the TASEP with periodic initial configuration , J. Stat. Phys. 129
2007
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2010
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T. Kriecherbauer and J. Krug, A pedestrian’s view on interacting particle systems, KPZ universality, and random matrices , J. Phys. A 43
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T. Alberts, K. Khanin, J. Quastel, Intermediate disorder regime for directed polymers in dimension 1+1 , Phys. Rev. Lett. 105
2010
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F. Bornemann, On the numerical evaluation of Fredholm determinants , Math. Comp., 79
2010
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T. Sasamoto and H. Spohn, One-dimensional Kadar-Parisi-Zhang equation: an exact solution and its universality , Phys. Rev. Lett. 104
2010
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T. Sasamoto, H. Spohn, Exact height distributions for the KPZ equation with narrow wedge initial condition , Nuclear Phys. B 834
2010
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T. Sasamoto, H. Spohn, The crossover regime for the weakly asymmetric simple exclusion process , J. Stat. Phys. 128
2010
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V. Dotsenko and B. Klumov, Bethe ansatz solution for one-dimensional directed polymers in random media , J. Stat. Mech. (2010), P03022
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V. Dotsenko, Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers , J. Stat. Mech. (2010), P07010
2010
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P. Calabrese, P. Le Doussal, A. Rosso, Free-energy distribution of the directed polymer at high temperature , EPL 90
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V. Dotsenko, Bethe ansatz derivation of the Tracy-Widom distribution for one-dimensional directed polymers , EPL 90
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