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We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\beta$-ensembles.
Singular integral equations
N. I. Muskhelishvili · 1992
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On the statistical mechanics approach in the random matrix theory: integrated density of states
A. Boutet de Monvel, L. Pastur, and M. Shcherbina · 1995
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New results on the equilibrium measure for logarithmic potentials in the presence of an external field
P. Deift, T. Kriecherbauer, and K. T.-R. McLaughlin · 1998
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On fluctuations of eigenvalues of random Hermitian matrices
K. Johansson · 1998
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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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Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields
A. Kuijlaars and K. McLaughlin · 2000
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Universality of the double scaling limit in random matrix models
T. Claeys and A.B.J. Kuijlaars · 2006
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Second order asymptotics for matrix models
A. Guionnet and E. Maurel-Segala · 2007
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Birth of a cut in unitary random matrix ensembles
T. Claeys · 2008
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The Riemann–Hilbert approach to double scaling limit of random matrix eigenvalues near the ”birth of a cut” transition
M.Y. Mo · 2008
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Higher-order analogues of the Tracy-Widom distribution and the Painlevé ii hierarchy
T. Claeys, I. Krasovsky, and A. Its · 2010
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Log-gases and random matrices
P. Forrester · 2010
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Transport maps for β \beta -matrix models and universality
F. Bekerman, A. Figalli, and A. Guionnet · 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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Fluctuations of linear eigenvalue statistics of β \beta matrix models in the multi-cut regime
M. Shcherbina · 2013
Free transport-entropy inequalities for non-convex potentials and application to concentration for random matrices
M. Maï da and É. Maurel-Segala · 2014
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Next order asymptotics and renormalized energy for riesz interactions
M. Petrache and S. Serfaty · 2014
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Change of variables as a method to study general β \beta -models: bulk universality
M. Shcherbina · 2014
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Large deviation principle for empirical fields of Log and Riesz gases
T. Leblé and S. Serfaty · 2015
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1D log gases and the renormalized energy: crystallization at vanishing temperature
É. Sandier and S. Serfaty · 2015
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Mesoscopic central limit theorem for general β \beta -ensembles
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Universality of general β \beta -ensembles
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Free monotone transport
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Fluctuations of two-dimensional Coulomb gases
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Quantitative stochastic homogenization and large-scale regularity
S. Armstrong, T. Kuusi, and J.-C. Mourrat · 2017
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Stein’s method for normal approximation of linear statistics of beta-ensembles
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