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We prove that under n^{1/3} scaling, the limiting distribution as n goes to infinity of the free energy of Seppalainen's log-Gamma discrete directed polymer is GUE Tracy-Widom.
Handbook of mathematical functions with formulas, graphs, and mathematical tables
M. Abramowitz and I. A. Stegun · 1964
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Level-spacing distributions and the Airy kernel
C. Tracy, H. Widom · 1994
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Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
J. Baik, G. Ben Arous, S. Peché · 2006
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Airy kernel with two sets of parameters in directed percolation and random matrix theory
A. Borodin, S. Péché · 2008
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Asymptotics in ASEP with step initial condition
C. Tracy, H. Widom · 2009
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Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 1+1 dimensions
G. Amir, I. Corwin, J. Quastel · 2011
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A. Borodin and I. Corwin · 2011
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Tropical combinatorics and Whittaker functions
I. Corwin, N. O’Connell, T. Seppäläinen, and N. Zygouras · 2011
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Intermediate disorder regime for 1+1 dimensional directed polymers
T. Alberts, K. Khanin, J. Quastel · 2012
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Universality for directed polymers in thin rectangles
A. Auffinger, J. Baik, I. Corwin · 2012
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Note sur une relation entre les intégrales définies des produits des fonctions
C. Andréief
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Universal distribution of fluctuations at the edge of the rarefaction fan
I. Corwin, J. Quastel
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In preparation
G. Moreno Flores, J. Quastel, D. Remenik
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Free energy fluctuations for directed polymers in random media in 1+1 dimension
A. Borodin, I. Corwin, and P. Ferrari · 2012
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The Kardar-Parisi-Zhang equation and universality class
I. Corwin · 2012
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Directed polymers and the quantum Toda lattice
N. O’Connell · 2012
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Scaling for a one-dimensional directed polymer with boundary
T. Seppäläinen · 2012
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