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We establish a fundamental connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions, analogous to the well known relationship between the RSK correspondence and Schur functions.
An extension of Schensted’s theorem
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Quantisation and representation theory. In: Representation Theory of Lie Groups
B. Kostant · 1977
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A variational problem for random Young tableaux
B. F. Logan, L. A. Shepp · 1977
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Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tables
A. M. Vershik, S. Kerov · 1977
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Markov functions
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M. Semenov-Tian-Shansky · 1994
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Level-spacing distributions and the Airy kernel
C. Tracy and H. Widom · 1994
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I. Macdonald · 1995
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A. Givental · 1997
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T. Seppäläinen · 1998
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D. Aldous, P. Diaconis · 1999
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On the distribution of the length of the longest increasing subsequence of random permutations
J. Baik, P.A. Deift, K. Johansson · 1999
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A version of Pitman’s 2 M − X 2M-X theorem for geometric Brownian motions
H. Matsumoto, M. Yor · 1999
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Exact limiting shape for a simplified model of first-passage percolation on the plane
T. Seppäläinen · 1999
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Shape fluctuations and random matrices
K. Johansson · 2000
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The Robinson-Schensted-Knuth bijection, quantum matrices and piece-wise linear combinatorics
A. Berenstein, A.N. Kirillov · 2001
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Discrete orthogonal polynomial ensembles and the Plancherel measure
K. Johansson · 2001
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Integral representations for the eigenfunctions of quantum open and periodic Toda chains from the QISM formalism
S. Kharchev, D. Lebedev · 2001
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Introduction to tropical combinatorics
A. N. Kirillov · 2001
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Brownian analogues of Burke’s theorem
N. O’Connell, M. Yor · 2001
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Infinite wedge and random partitions
A. Okounkov · 2001
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Paths in Weyl chambers and random matrices
Ph. Bougerol, Th. Jeulin · 2002
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Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles
W. König, N. O’Connell, S. Roch · 2002
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Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices
P. J. Forrester, E. M. Rains · 2006
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On a Gauss-Givental representation of quantum Toda chain wave equation
A. Gerasimov, S. Kharchev, D. Lebedev, S. Oblezin · 2006
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A mirror construction for the totally nonnegative part of the Peterson variety
K. Rietsch · 2006
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Lecture notes on geometric crystals and their combinatorial analogues
A. Berenstein, D. Kazhdan · 2007
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The octahedron recurrence and RSK-correspondence
V. Danilov, G. Koshevoy · 2007
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On the free energy of a directed polymer in a Brownian environment
J. Moriarty, N. O’Connell · 2007
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Random matrices, non-colliding processes and queues
N. O’Connell · 2002
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A representation for non-colliding random walks
N. O’Connell, M. Yor · 2002
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Archimedean L L -factors on G L ( n ) × G L ( n ) GL(n)\times GL(n) and generalized Barnes integrals
E. Stade · 2002
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A note on representations of eigenvalues of classical Gaussian matrices
Y. Doumerc, · 2003
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Conditioned random walks and the RSK correspondence
N. O’Connell · 2003
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A path-transformation for random walks and the Robinson-Schensted correspondence
N. O’Connell · 2003
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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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Baxter Operator and Archimedean Hecke Algebra
A. Gerasimov, D. Lebedev, S. Oblezin · 2008
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Continuous crystals and Duistermaat-Heckman measure for Coxeter groups
Ph. Biane, Ph. Bougerol, N. O’Connell · 2009
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On the largest-eigenvalue process for generalized Wishart random matrices
A.B. Dieker, J. Warren · 2009
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Order of current variance and diffusivity in the asymmetric simple exclusion process
M. Balázs, T. Seppäläinen · 2010
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Geometric and unipotent crystals
A. Berenstein, D. Kazhdan · 2010
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Orbit measures, random matrix theory and interlaced determinantal processes
M. Defosseux · 2010
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The 1 + 1 1+1 -dimensional Kardar-Parisi-Zhang equation and its universality class
T. Sasamoto, H. Spohn · 2010
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Bounds for scaling exponents for a 1+1 dimensional directed polymer in a Brownian environment
T. Seppäläinen, B. Valko · 2010
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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 conditions
T. Seppäläinen · 2012
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