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The link between a particular class of growth processes and random matrices was established in the now famous 1999 article of Baik, Deift, and Johansson on the length of the longest increasing subsequence of a random permutation.
Dimer statistics and phase transitions
P.W. Kasteleyn · 1963
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Interaction of Markov processes
F. Spitzer · 1970
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Kinetics of Ising models
K. Kawasaki · 1972
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Aspects of first-passage percolation
H. Kesten · 1986
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Dynamic scaling of growing interfaces
K. Kardar, G. Parisi, and Y.Z. Zhang · 1986
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Unitary-matrix models as exactly solvable string theories
V. Perival and D. Shevitz · 1990
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Large Scale Dynamics of Interacting Particles
H. Spohn · 1991
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Alternating-Sign Matrices and Domino Tilings I and II
N. Elkies, G. Kuperbert, M. Larsen, and J. Propp · 1992
Earlier work this paper cites.
The six-vertex model, roughened surfaces and an asymmetric spin Hamiltonian
L-H. Gwa and H. Spohn · 1992
Earlier work this paper cites.
Fractal Concepts in Surface Growth
A.L. Barabási and H.E. Stanley · 1995
Earlier work this paper cites.
Local statistics for random domino tilings of the Aztec diamond
H. Cohn, N. Elkies, and J. Propp · 1996
Earlier work this paper cites.
An Exactly Solved Model of Three Dimensional Surface Growth in the Anisotropic KPZ Regime
M. Prähofer and H. Spohn · 1997
Earlier work this paper cites.
Exact solution of the master equation for the asymmetric exclusion process
G.M. Schütz · 1997
Earlier work this paper cites.
Matrices coupled in a chain. I. Eigenvalue correlations
B. Eynard and M.L. Mehta · 1998
Earlier work this paper cites.
Random domino tilings and the arctic circle theorem
W. Jockush, J. Propp, and P. Shor · 1998
Earlier work this paper cites.
On growth, disorder, and field theory
M. Lässig · 1998
Earlier work this paper cites.
Fractals, Scaling and Growth Far From Equilibrium
P. Meakin · 1998
Earlier work this paper cites.
Multilevel dynamical correlation functions for Dysons Brownian motion model of random matrices
T. Nagao and P.J. Forrester · 1998
Earlier work this paper cites.
On the distribution of the length of the longest increasing subsequence of random permutations
J. Baik, P.A. Deift, and K. Johansson · 1999
Earlier work this paper cites.
Scaling Limits of Interacting Particle Systems
C. Kipnis and C. Landim · 1999
Earlier work this paper cites.
Stochastic Interacting Systems: Contact, Voter and Exclusion Processes
T.M. Liggett · 1999
Earlier work this paper cites.
Limiting distributions for a polynuclear growth model with external sources
J. Baik and E.M. Rains · 2000
Earlier work this paper cites.
Shape fluctuations and random matrices
K. Johansson · 2000
Earlier work this paper cites.
The planar dimer model with boundary: a survey
R. Kenyon · 2000
Earlier work this paper cites.
Thermodynamic limit of the six-vertex model with domain wall boundary conditions
V. Korepin and P. Zinn-Justin · 2000
Cited alongside, same era.
Statistical self-similarity of one-dimensional growth processes
M. Prähofer and H. Spohn · 2000
Cited alongside, same era.
Universal distributions for growth processes in 1 + 1 1+1 dimensions and random matrices
M. Prähofer and H. Spohn · 2000
Cited alongside, same era.
Algebraic aspects of increasing subsequences
J. Baik and E.M. Rains · 2001
Cited alongside, same era.
The asymptotics of monotone subsequences of involutions
J. Baik and E.M. Rains · 2001
Cited alongside, same era.
The low-temperature expansion of the Wulff crystal in the 3D-Ising model
R. Cerf and R. Kenyon · 2001
Cited alongside, same era.
One-dimensional stochastic growth and Gaussian ensembles of random matrices
P.L. Ferrari and M. Prähofer · 2006
Later among the works it cites.
Domino tilings and the six-vertex model at its free fermion point
P.L. Ferrari and H. Spohn · 2006
Later among the works it cites.
Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process
P.L. Ferrari and H. Spohn · 2006
Later among the works it cites.
Eigenvalues of GUE minors
K. Johansson and E. Nordenstam · 2006
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Random matrices and determinantal processes
K. Johansson · 2006
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Dimers and amoebae
R. Kenyon, A. Okounkov, and S. Sheffield · 2006
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Current fluctuations for the totally asymmetric simple exclusion process
M. Prähofer and H. Spohn · 2002
Cited alongside, same era.
Scale invariance of the PNG droplet and the Airy process
M. Prähofer and H. Spohn · 2002
Cited alongside, same era.
Step fluctations for a faceted crystal
P.L. Ferrari and H. Spohn · 2003
Cited alongside, same era.
Discrete polynuclear growth and determinantal processes
K. Johansson · 2003
Cited alongside, same era.
Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
A. Okounkov and N. Reshetikhin · 2003
Cited alongside, same era.
Generalized Domino-Shuffling
J. Propp · 2003
Cited alongside, same era.
The birth of a random matrix
A. Okounkov and N. Reshetikhin · 2006
Later among the works it cites.
Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
H. Spohn · 2006
Later among the works it cites.
Fluctuation properties of the TASEP with periodic initial configuration
A. Borodin, P.L. Ferrari, M. Prähofer, and T. Sasamoto · 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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Random skew plane partitions and the Pearcey process
A. Okounkov and N. Reshetikhin · 2007
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Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques
T. Sasamoto · 2007
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Dyson’s Brownian motions, intertwining and interlacing
Jon Warren · 2007
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Anisotropic growth of random surfaces in 2 + 1 2+1 dimensions
A. Borodin and P.L. Ferrari · 2008
Later among the works it cites.
Large time asymptotics of growth models on space-like paths I: PushASEP
A. Borodin and P.L. Ferrari · 2008
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The 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 II: PNG and parallel TASEP
A. Borodin, P.L. Ferrari, and T. Sasamoto · 2008
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The universal Airy 1 and Airy 2 processes in the Totally Asymmetric Simple Exclusion Process
P.L. Ferrari · 2008
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Height fluctuations in the honeycomb dimer model
R. Kenyon · 2008
Later among the works it cites.
Interacting particle systems out of equilibrium
T. Kriecherbauer and J. Krug · 2008
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On the shuffling algorithm for domino tilings
E. Nordenstam · 2008
Later among the works it cites.
Integral Formulas for the Asymmetric Simple Exclusion Process
C.A. Tracy and H. Widom · 2008
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Asymptotics in ASEP with step initial condition
C.A. Tracy and H. Widom · 2009
Later among the works it cites.
Limit process of stationary TASEP near the characteristic line
J. Baik, P.L. Ferrari, and S. Péché · 2010
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