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We study discrete $\beta$-ensembles as introduced in [17].
Integral equations
F. G. Tricomi · 1957
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On the density of eigenvalues of a random matrix
M. L. Mehta and M. Gaudin · 1960
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Correlations between eigenvalues of a random matrix
Freeman J. Dyson · 1970
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A note on correlations between eigenvalues of a random matrix
M. L. Mehta · 1971
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A bound for the error in the normal approximation to the distribution of a sum of dependent random variables
Charles Stein · 1972
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Eine Klasse von p p -Gruppen, deren Automorphismengruppen p p -Gruppen sind
W. Lindenberg · 1974
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Level-spacing distributions and the Airy kernel
Craig A. Tracy and Harold Widom · 1994
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On orthogonal and symplectic matrix ensembles
Craig A. Tracy and Harold Widom · 1996
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Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy
G. Ben Arous and A. Guionnet · 1997
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A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanics
Percy A. Deift, Alexander R. Its, and Xin Zhou · 1997
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Constrained energy problems with applications to orthogonal polynomials of a discrete variable
P. D. Dragnev and E. B. Saff · 1997
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Universality of the local eigenvalue statistics for a class of unitary invariant matrix ensembles
L. Pastur and M. Shcherbina · 1997
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The shape of a typical boxed plane partition
Henry Cohn, Michael Larsen, and James Propp · 1998
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On fluctuations of eigenvalues of random Hermitian matrices
K. Johansson · 1998
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On the distribution of the length of the longest increasing subsequence of random permutations
Jinho Baik, Percy Deift, and Kurt Johansson · 1999
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Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
Pavel Bleher and Alexander Its · 1999
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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou · 1999
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Universality at the edge of the spectrum in Wigner random matrices
Alexander Soshnikov · 1999
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Asymptotics of Plancherel measures for symmetric groups
Alexei Borodin, Andrei Okounkov, and Grigori Olshanski · 2000
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Asymptotics of Plancherel measures for symmetric groups
Alexei Borodin, Andrei Okounkov, and Grigori Olshanski · 2000
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Shape fluctuations and random matrices
Kurt Johansson · 2000
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Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields
A. B. J. Kuijlaars and K. T-R McLaughlin · 2000
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Random matrices and random permutations
Andrei Okounkov · 2000
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The asymptotics of monotone subsequences of involutions
Jinho Baik and Eric M. Rains · 2001
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z z -measures on partitions, Robinson-Schensted-Knuth correspondence, and β = 2 \beta=2 random matrix ensembles
Alexei Borodin and Grigori Olshanski · 2001
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Discrete orthogonal polynomial ensembles and the Plancherel measure
Kurt Johansson · 2001
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Discrete orthogonal polynomial ensembles and the Plancherel measure
Kurt Johansson · 2001
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Matrix models for beta ensembles
Ioana Dumitriu and Alan Edelman · 2002
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Non-intersecting paths, random tilings and random matrices
Kurt Johansson · 2002
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Non-colliding random walks, tandem queues, and discrete orthogonal polynomial ensembles
Wolfgang König, Neil O’Connell, and Sébastien Roch · 2002
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Uniform asymptotics for polynomials orthogonal with respect to a general class of discrete weights and universality results for associated ensembles: announcement of results
J. Baik, T. Kriecherbauer, K. D. T.-R. McLaughlin, and P. D. Miller · 2003
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Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
Andrei Okounkov and Nikolai Reshetikhin · 2003
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Probability measures on dual objects to compact symmetric spaces, and hypergeometric identities
G. I. Ol ′ \prime shanskiĭ · 2003
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Stein’s method, Jack measure, and the Metropolis algorithm
Jason Fulman · 2004
Cited alongside, same era.
Random matrices
M. L. Mehta · 2004
Cited alongside, same era.
Z Z -measures on partitions and their scaling limits
Alexei Borodin and Grigori Olshanski · 2005
Cited alongside, same era.
The arctic circle boundary and the Airy process
Kurt Johansson · 2005
Cited alongside, same era.
The uses of random partitions
Andrei Okounkov · 2005
Cited alongside, same era.
Discrete orthogonal polynomials
J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin, and P. D. Miller · 2007
Cited alongside, same era.
Asymptotics of Plancherel-type random partitions
Alexei Borodin and Grigori Olshanski · 2007
Scaling for a one-dimensional directed polymer with boundary conditions
Timo Seppäläinen · 2012
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Fluctuations of linear eigenvalue statistics of β \beta matrix models in the multi-cut regime
M. Shcherbina · 2012
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Log-gamma polymer free energy fluctuations via a Fredholm determinant identity
Alexei Borodin, Ivan Corwin, and Daniel Remenik · 2013
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Asymptotic Expansion of β \beta Matrix Models in the multi-cut Regime
G. Borot and A. Guionnet · 2013
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Asymptotic Expansion of β \beta Matrix Models in the one-cut Regime
G. Borot and A. Guionnet · 2013
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Cited alongside, same era.
Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
P.A. Deift and D. Gioev · 2007
Cited alongside, same era.
Universality in random matrix theory for orthogonal and symplectic ensembles
P.A. Deift and D. Gioev · 2007
Cited alongside, same era.
On large deviations for the spectral measure of discrete Coulomb gas
D. Féral · 2008
Cited alongside, same era.
Nonintersecting paths and the Hahn orthogonal polynomial ensemble
V. E. Gorin · 2008
Cited alongside, same era.
Universality limits in the bulk for varying measures
E. Levin and D. S. Lubinsky · 2008
Cited alongside, same era.
Spectral statistics of Erdős-Rényi graphs I: Local semicircle law
László Erdős, Antti Knowles, Horng-Tzer Yau, and Jun Yin · 2013
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Eigenvector distribution of Wigner matrices
Antti Knowles and Jun Yin · 2013
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Quantum geometry and quiver gauge theories
N. Nekrasov, V Pestun, and S. Shatashvili · 2013
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Change of variables as a method to study general β \beta -models: bulk universality
M. Shcherbina · 2013
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Random matrices: sharp concentration of eigenvalues
Terence Tao and Van Vu · 2013
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From duality to determinants for q q -TASEP and ASEP
Alexei Borodin, Ivan Corwin, and Tomohiro Sasamoto · 2014
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Anisotropic growth of random surfaces in 2 + 1 2+1 dimensions
Alexei Borodin and Patrik L. Ferrari · 2014
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Integrable probability: from representation theory to Macdonald processes
Alexei Borodin and Leonid Petrov · 2014
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Edge universality of beta ensembles
Paul Bourgade, László Erdös, and Horng-Tzer Yau · 2014
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Universality of general β \beta -ensembles
Paul Bourgade, László Erdős, and Horng-Tzer Yau · 2014
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Convergence of local statistics of Dyson Brownian motion
Benjamin Landon and Horng-Tzer Yau · 2014
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A necessary and sufficient condition for edge universality of Wigner matrices
Ji Oon Lee and Jun Yin · 2014
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Asymptotics of random lozenge tilings via Gelfand-Tsetlin schemes
Leonid Petrov · 2014
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Transport maps for β \beta -matrix models and universality
F. Bekerman, A. Figalli, and A. Guionnet · 2015
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Discrete time q q -TASEPs
Alexei Borodin and Ivan Corwin · 2015
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Large- N N asymptotic expansion for mean field models with Coulomb gas interaction
Gaëtan Borot, Alice Guionnet, and Karol K. Kozlowski · 2015
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Local microscopic behavior for 2d coulomb gases
Thomas Leblé · 2015
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Asymptotics of uniformly random lozenge tilings of polygons. Gaussian free field
Leonid Petrov · 2015
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Mesoscopic central limit theorem for general β \beta -ensembles
F. Bekerman and A. Lodhia · 2016
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Transport maps for β \beta -matrix models in the multi-cut regime
Florent Bekerman · 2016
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Gaussian asymptotics of discrete β \beta -ensembles
Alexei Borodin, Vadim Gorin, and Alice Guionnet · 2016
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Fluctuations of particle systems determined by schur generating functions
A. Bufetov and V. Gorin · 2016
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Gaussian fluctuations of Young diagrams and structure constants of Jack characters
Maciej Dołęga and Valentin Féray · 2016
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Universality of the stochastic Airy operator
Manjunath Krishnapur, Brian Rider, and Bálint Virág · 2016
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Local law and tracy-widom limit for sparse random matrices
Ji Oon Lee and Kevin Schnelli · 2016
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Bulk universality for deformed Wigner matrices
Ji Oon Lee, Kevin Schnelli, Ben Stetler, and Horng-Tzer Yau · 2016
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Fluctuations for multi-cut discrete β \beta –ensembles and application to random tilings
G. Borot, V. Gorin, and A. Guionnet · 2017
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Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients
Jonathan Breuer and Maurice Duits · 2017
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