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These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists.
The partial differential equation u t + u u x = μ u x x u_{t}+uu_{x}=\mu u_{xx}
E. Hopf · 1950
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On a quasi-linear parabolic equation occurring in aerodynamics
J.D. Cole · 1951
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Permutations, matrices, and generalized Young tableaux
D. E. Knuth · 1970
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Interaction of Markov processes
F. Spitzer · 1970
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Large-distance and long-time properties of a randomly stirred fluid
D. Forster, D. R. Nelson, and M. J. Stephen · 1977
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Reversibility and stochastic networks
F. Kelly · 1979
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Non-equilibrium behaviour of a many particle process: Density profile and local equilibria
H. Rost · 1981
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Long range correlations for stochastic lattice gases in a non-equilibrium steady state
H. Spohn · 1983
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Statistical mechanics of cellular automata
S. Wolfram · 1983
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Huse, Henley, and Fisher respond
D. A. Huse, C. L. Henley, and D. S. Fisher · 1985
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Excess noise for driven diffusive systems
H. van Beijeren, R. Kutner, and H. Spohn · 1985
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Dynamic scaling of growing interfaces
M. Kardar, G. Parisi, and Y.-C. Zhang · 1986
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Ballistic deposition on surfaces
P. Meakin, P. Ramanlal, L. M. Sander, and R. C. Ball · 1986
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Stationary measures for an exclusion process on one-dimensional lattices with infinitely many hopping sites
H. Yaguchi · 1986
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Replica Bethe ansatz studies of two-dimensional interfaces with quenched random impurities
M. Kardar · 1987
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Scaling of directed polymers in random media
M. Kardar and Y.-C. Zhang · 1987
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Time-reversal invariance and universality of two-dimensional growth models
M. Plischke, Z. Rácz, and D. Liu · 1987
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Universality classes for deterministic surface growth
J. Krug and H. Spohn · 1988
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Microscopic models of hydrodynamic behavior
J. L. Lebowitz, E. Presutti, and H. Spohn · 1988
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The weakly asymmetric simple exclusion process
A. DeMasi, E. Presutti, and E. Scacciatelli · 1989
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Anomalous fluctuations in the driven and damped sine-Gordon chain
J. Krug and H. Spohn · 1989
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Dynamics of an anchored Toom interface
B. Derrida, J. L. Lebowitz, E. R. Speer, and H. Spohn · 1991
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Microscopic structure of travelling waves in the asymmetric simple exclusion process
P. A. Ferrari, C. Kipnis, and E. Saada · 1991
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Boundary-induced phase transitions in driven diffusive systems
J. Krug · 1991
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Kinetic roughening of growing surfaces
J. Krug and H. Spohn · 1991
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Large scale dynamics of interacting particles
H. Spohn · 1991
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Universality in surface growth - scaling functions and amplitude ratios
J. G. Amar and F. Family · 1992
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Universality class of interface growth with reflection symmetry
P. Devillard and H. Spohn · 1992
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Shock fluctuations in asymmetric simple exclusion
P. A. Ferrari · 1992
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Amplitude universality for driven interfaces and directed polymers in random media
J. Krug, P. Meakin, and T. Halpin-Healy · 1992
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Exact solution of the totally asymmetric exclusion process: Shock profiles
B. Derrida, S. A. Janowsky, J. L. Lebowitz, and E. R. Speer · 1993
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Cellular-automaton models and traffic flow
A. Schadschneider and M. Schreckenberg · 1993
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Scaling of fluctuations in one-dimensional interface and hopping models
P. M. Binder, M. Paczuski, and M. Barma · 1994
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Theory of phase-ordering kinetics
A. J. Bray · 1994
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Disorder-induced unbinding in confined geometries
J. Krug and L.-H. Tang · 1994
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Level-spacing distributions and the Airy kernel
C. A. Tracy and H. Widom · 1994
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Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics
T. Halpin-Healy and Y.-C. Zhang · 1995
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Experimental observations of self-affine scaling and kinetic roughening at submicron lengthscales
J. Krim and G. Palasantzas · 1995
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Statistical mechnics of driven diffusive systems
B. Schmittmann and R. K. P. Zia · 1995
Earlier work this paper cites.
Discrete stochastic models for traffic flow
M. Schreckenberg, A. Schadschneider, K. Nagel, and N. Ito · 1995
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Mode-coupling and renormalization group results for the noisy Burgers equation
E. Frey, U. C. Täuber, and T. Hwa · 1996
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Pairwise balance and invariant measures for generalized exclusion processes
G. M. Schütz, R. Ramaswamy, and M. Barma · 1996
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Stochastic Burgers and KPZ equations from particle systems
L. Bertini and G. Giacomin · 1997
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Short-time scaling behavior of growing interfaces
M. Krech · 1997
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Origins of scale invariance in growth processes
J. Krug · 1997
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Kinetic roughening in slow combustion of paper
J. Maunuksela, M. Myllys, O.-P. Kähkönen, J. Timonen, N. Provatas, M. J. Alava, and T. Ala-Nissila · 1997
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Exact solution of the master equation for the asymmetric exclusion process
G. M. Schütz · 1997
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Fluctuations of a surface submitted to a random average process
P. A. Ferrari and L. R. G. Fontes · 1998
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Ground-state energy anisotropy for directed polymers in random media
J. Krug and T. Halpin-Healy · 1998
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Correlation functions, cluster functions, and spacing distributions for random matrices
C. A. Tracy and H. Widom · 1998
Cited alongside, same era.
Longest increasing subsequences: from patience sorting to the Baik-Deift-Johansson theorem
D. Aldous and P. Diaconis · 1999
Cited alongside, same era.
On the distribution of the length of the longest increasing subsequence of random permutations
J. Baik, P. Deift, and K. Johansson · 1999
Cited alongside, same era.
Orthogonal polynomials and random matrices: a Riemann-Hilbert approach
P. Deift · 1999
Cited alongside, same era.
Strong asymptotics of orthogonal polynomials with respect to exponential weights
Discrete orthogonal polynomials
J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin, and P. D. Miller · 2007
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Stochastic interacting particle systems out of equilibrium
L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, and C. Landim · 2007
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Nonequilibrium steady states of matrix-product form: a solver’s guide
R. A. Blythe and M. R. Evans · 2007
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Fluctuation properties of the TASEP with periodic initial configuration
A. Borodin, P. L. Ferrari, M. Prähofer, and T. Sasamoto · 2007
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Universality for mathematical and physical systems
P. Deift · 2007
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Non-equilibrium steady states: fluctuations and large deviations of the density and of the current
B. Derrida · 2007
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P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou · 1999
Cited alongside, same era.
Persistence of Kardar-Parisi-Zhang interfaces
H. Kallabis and J. Krug · 1999
Cited alongside, same era.
Scaling limits of interacting particles systems
C. Kipnis and C. Landim · 1999
Cited alongside, same era.
Stochastic interacting systems: contact, voter and exclusion processes
T. M. Liggett · 1999
Cited alongside, same era.
Existence of hydrodynamics for the totally asymmetric simple k-exclusion process
T. Seppäläinen · 1999
Cited alongside, same era.
Limiting distributions for a polynuclear growth model with external sources
J. Baik and E. M. Rains · 2000
Cited alongside, same era.
Statistical physics of vehicular traffic and some related systems
D. Chowdhury, L. Santen, and A. Schadschneider · 2000
Cited alongside, same era.
Random matrices, the Ulam problem, directed polymers & growth models, and sequence matching
S. N. Majumdar · 2007
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t 1 / 3 t^{1/3} Superdiffusivity of finite-range asymmetric exclusion processes on ℤ \mathbb{Z}
J. Quastel and B. Valkó · 2007
Later among the works it cites.
Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
T. Sasamoto · 2007
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Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
R. K. P. Zia and B. Schmittmann · 2007
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Microscopic concavity and fluctuation bounds in a class of deposition processes
M. Balázs, J. Komjáthy, and T. Seppäläinen · 2008
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The Airy 1 {\rm Airy}_{1} process is not the limit of the largest eigenvalue in GOE matrix diffusion
F. Bornemann, P. L. Ferrari, and M. Prähofer · 2008
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Large time asymptotics of growth models on space-like paths. I. PushASEP
A. Borodin and P. L. Ferrari · 2008
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Transition between Airy 1 {\rm Airy}_{1} and Airy 2 {\rm Airy}_{2} processes and TASEP fluctuations
A. Borodin, P. L. Ferrari, and T. Sasamoto · 2008
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Slow decorrelations in Kardar-Parisi-Zhang growth
P. L. Ferrari · 2008
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The universal Airy 1 {\rm Airy}_{1} and Airy 2 {\rm Airy}_{2} processes in the totally asymmetric simple exclusion process
P. L. Ferrari · 2008
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Universality limits in the bulk for arbitrary measures on compact sets
D. S. Lubinsky · 2008
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The ∂ ¯ \overline{\partial} steepest descent method for orthogonal polynomials on the real line with varying weights
K. T.-R. McLaughlin and P. D. Miller · 2008
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A note on the diffusivity of finite-range asymmetric exclusion processes on ℤ \mathbb{Z}
J. Quastel and B. Valkó · 2008
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A Fredholm determinant representation in ASEP
C. A. Tracy and H. Widom · 2008
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Integral formulas for the asymmetric simple exclusion process
C. A. Tracy and H. Widom · 2008
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Nonintersecting Brownian motions, integrable systems and orthogonal polynomials
P. van Moerbeke · 2008
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Current fluctuations for TASEP: A proof of the Prähofer-Spohn conjecture
G. Ben Arous and I. Corwin · 2009
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Fluctuation bounds for the asymmetric simple exclusion process
M. Balázs and T. Seppäläinen · 2009
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On the numerical evaluation of distributions in random matrix theory: a review
F. Bornemann · 2009
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Random matrix theory: invariant ensembles and universality
P. Deift and D. Gioev · 2009
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On the Airy reproducing kernel, sampling series, and quadrature formula
E. Levin and D. S. Lubinsky · 2009
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Universality limits for random matrices and de Branges spaces of entire functions
D. S. Lubinsky · 2009
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Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation
T. Sasamoto and H. Spohn · 2009
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Asymptotics in ASEP with step initial condition
C. A. Tracy and H. Widom · 2009
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On ASEP with step Bernoulli initial condition
C. A. Tracy and H. Widom · 2009
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On the distribution of a second-class particle in the asymmetric simple exclusion process
C. A. Tracy and H. Widom · 2009
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Total current fluctuations in the asymmetric simple exclusion process
C. A. Tracy and H. Widom · 2009
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Probability distribution of the free energy of the continuum directed random polymer in 1+1 dimensions
G. Amir, I. Corwin, and J. Quastel · 2010
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Limit process of stationary TASEP near the characteristic line
J. Baik, P. L. Ferrari, and S. Péché · 2010
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Scaling exponent for the Hopf-Cole solution of KPZ/stochastic Burgers
M. Balázs, J. Quastel, and T. Seppäläinen · 2010
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Order of current variance and diffusivity in the asymmetric simple exclusion process
M. Balázs and T. Seppäläinen · 2010
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Free energy distribution of the directed polymer at high temperature
P. Calabrese, P. Le Doussal, and A. Rosso · 2010
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Limit processes for TASEP with shocks and rarefaction fans
I. Corwin, P. L. Ferrari, and S. Péché · 2010
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Universality of slow decorrelation in KPZ growth
I. Corwin, P. L. Ferrari, and S. Péché · 2010
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Bethe ansatz derivation of the Tracy-Widom distribution for one-dimensional directed polymers
V. Dotsenko · 2010
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Universality of Wigner random matrices: a survey of recent results
L. Erdős · 2010
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The crossover regime for the weakly asymmetric simple exclusion process
T. Sasamoto and H. Spohn · 2010
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Exact height distributions for the KPZ equation with narrow wedge initial condition
T. Sasamoto and H. Spohn · 2010
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One-dimensional Kardar-Parisi-Zhang equation: An exact solution and its universality
T. Sasamoto and H. Spohn · 2010
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Universal fluctuations of growing interfaces: Evidence in turbulent liquid crystals
K. A. Takeuchi and M. Sano · 2010
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Formulas for ASEP with two-sided Bernoulli initial condition
C. A. Tracy and H. Widom · 2010
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