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We show that the supremum of the average of the Airy process and its time reversal minus a parabola is distributed as the maximum of two independent GUE Tracy-Widom random variables.
A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation
S. P. Hastings and J. B. McLeod · 1980
Earlier work this paper cites.
Level-spacing distributions and the Airy kernel
C. A. Tracy and H. Widom · 1994
Earlier work this paper cites.
On orthogonal and symplectic matrix ensembles
C. A. Tracy and H. Widom · 1996
Earlier work this paper cites.
Longest increasing subsequences of random colored permutations
A. Borodin · 1999
Earlier work this paper cites.
Random unitary matrices, permutations and Painlevé
C. A. Tracy and H. Widom · 1999
Earlier work this paper cites.
Limiting distributions for a polynuclear growth model with external sources
J. Baik and E. Rains · 2000
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Shape fluctuations and random matrices
K. Johansson · 2000
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Transversal fluctuations for increasing subsequences on the plane
K. Johansson · 2000
Earlier work this paper cites.
Optimal tail estimates for directed last passage site percolation with geometric random variables
J. Baik, P. Deift, K. T.-R. McLaughlin, P. Miller, and X. Zhou · 2001
Earlier work this paper cites.
The asymptotics of monotone subsequences of involutions
J. Baik and E. M. Rains · 2001
Cited alongside, same era.
Symmetrized random permutations
J. Baik and E. M. Rains · 2001
Cited alongside, same era.
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.
Discrete polynuclear growth and determinantal processes
K. Johansson · 2003
Cited alongside, same era.
Fluctuations of the one-dimensional polynuclear growth model in half-space
T. Sasamoto and T. Imamura · 2004
Cited alongside, same era.
Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
T. Imamura and T. Sasamoto · 2007
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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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On the joint distribution of the maximum and its position of the Airy 2 \rm Airy_{2} process minus a parabola
J. Baik, K. Liechty, and G. Schehr · 2012
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Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes, 2012
J. Baik and Z. Liu · 2012
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The Kardar-Parisi-Zhang equation and universality class
I. Corwin · 2012
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Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
J. Baik, G. Ben Arous, and S. Péché · 2005
Cited alongside, same era.
Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices
J. Baik · 2006
Cited alongside, same era.
Painlevé transcendents. The Riemann-Hilbert approach
A. S. Fokas, A. R. Its, A. A. Kapaev, and V. Y. Novokshenov · 2006
Cited alongside, same era.
in preparation
I. Corwin, Z. Liu, and D. Wang
Cited in the paper.
Airy processes and variational problems
J. Quastel and D. Remenik
Cited in the paper.
Extremes of N N vicious walkers for large N N : application to the directed polymer and KPZ interfaces
G. Schehr · 2012
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Continuum statistics of the Airy 2 {\rm Airy}_{2} process
I. Corwin, J. Quastel, and D. Remenik · 2013
Closest in time.
Endpoint distribution of directed polymers in 1 + 1 1+1 dimensions
G. Moreno Flores, J. Quastel, and D. Remenik · 2013
Closest in time.
Supremum of the Airy 2 \rm Airy_{2} process minus a parabola on a half line
J. Quastel and D. Remenik · 2013
Closest in time.