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These are the lecture notes of a course taught at the Park City Mathematics Institute in June 2017.
O. Frostman, Potentiel d’équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions. Meddelanden Mat. Sem. Univ. Lund 3
1935
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E. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. Math
1955
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A. Abrikosov, On the magnetic properties of superconductors of the second type. Soviet Phys. JETP 5
1957
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Diamètre transfini et comparaison de diverses capacités
G. Choquet · 1958
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F. Dyson, Statistical theory of the energy levels of a complex system. Part I, J. Math. Phys
1962
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J. Ginibre, Statistical ensembles of complex, quaternion, and real matrices. J. Math. Phys
1965
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Monte-Carlo study of a one-component plasma
S. G. Brush, H. L. Sahlin, and E. Teller · 1966
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E. H. Lieb, J. Lebowitz. The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei. Advances in Math
1972
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O. Penrose, E.R. Smith, Thermodynamic Limit for Classical Systems with Coulomb Interactions in a Constant External Field, Comm. Math. Phys
1972
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E. H. Lieb, H. Narnhofer, The thermodynamic limit for jellium. J. Statist. Phys
1975
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R. Sari, D. Merlini, On the ν \nu -dimensional one-component classical plasma: the thermodynamic limit problem revisited. J. Statist. Phys
1976
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A. Alastuey, B. Jancovici, On the classical two-dimensional one-component Coulomb plasma. J. Physique
1981
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A monte carlo study of the classical two-dimensional one-component plasma
J.-M. Caillol, D. Levesque, J.-J. Weis, and J.-P. Hansen · 1982
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P. Choquard and J. Clerouin. Cooperative phenomena below melting of the one-component two-dimensional plasma. Physical review letters
1983
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V. L. Girko, Circle law. Theory Probab. Appl
1984
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K. Huang, Statistical Mechanics
1987
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B. Jancovici, J. Lebowitz, G. Manificat, Large charge fluctuations in classical Coulomb systems. J. Statist. Phys
1993
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F. Bethuel, H. Brezis, F. Hélein, Ginzburg-Landau Vortices
1994
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B. Jancovici, Classical Coulomb systems: screening and correlations revisited. J. Statist. Phys
1995
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G. Ben Arous, A. Guionnet, Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy, Probab. Theory Related Fields
1997
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G. Ben Arous, A. Guionnet, Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy, Probab. Theory Related Fields
1997
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E.H. Lieb, M. Loss, Analysis, Graduate Studies in Mathematics 14
1997
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E. Saff, A. Kuijlaars, Distributing many points on a sphere. Math. Intelligencer
1997
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E. Saff, V. Totik, Logarithmic potentials with external fields
1997
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T. Spencer, Scaling, the free field and statistical mechanics, in The Legacy of Norbert Wiener: A. Centennial Symposium, Proc. Sympos. Pure Math
1997
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G. Ben Arous, O. Zeitouni, Large deviations from the circular law. ESAIM Probab. Statist
1998
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G. Ben Arous, O. Zeitouni, Large deviations from the circular law. ESAIM Probab. Statist
1998
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K. Johansson, On fluctuations of eigenvalues of random Hermitian matrices, Duke Math. J
1998
Cited alongside, same era.
D. Petz, F. Hiai, Logarithmic energy as an entropy functional, Advances in differential equations and mathematical physics
1998
Cited alongside, same era.
S. M. Stishov. Does the phase transition exist in the one-component plasma model? Jour. Exp. Theor. Phys. Lett
1998
Cited alongside, same era.
D. R. Adams, L. I. Hedberg, Function Spaces and Potential Theory
1999
Cited alongside, same era.
P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
1999
Cited alongside, same era.
H. Stormer, D. Tsui, A. Gossard, The fractional quantum Hall effect, Reviews of Modern Physics
S. Brauchart, D. Hardin, E. Saff, The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere. Recent advances in orthogonal polynomials, special functions, and their applications, 31?61, Contemp. Math., 578, Amer. Math. Soc., Providence, RI, 2012
2012
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E. Sandier, S. Serfaty, From the Ginzburg-Landau model to vortex lattice problems, Comm. Math. Phys
2012
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G. Borot, A. Guionnet, Asymptotic expansion of β \beta matrix models in the one-cut regime, Comm. Math. Phys
2013
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M. Shcherbina, Fluctuations of linear eigenvalue statistics of β \beta matrix models in the multi-cut regime, J. Stat. Phys. 151
2013
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D. Chafaï, N. Gozlan, P-A. Zitt, First-order global asymptotics for confined particles with singular pair repulsion. Ann. Appl. Probab
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1999
Cited alongside, same era.
I. Dumitriu, A. Edelman, Matrix models for beta ensembles, J. Math. Phys
2002
Cited alongside, same era.
S. Girvin, Introduction to the fractional quantum Hall effect, Séminaire Poincaré
2004
Cited alongside, same era.
R. Killip, I. Nenciu, Matrix models for circular ensembles. Int. Math. Res. Not
2004
Cited alongside, same era.
M. L. Mehta, Random matrices. Third edition
2004
Cited alongside, same era.
J. Barré, F. Bouchet, T. Dauxois, and S. Ruffo. Large deviation techniques applied to systems with long-range interactions. J. Stat. Phys
2005
Cited alongside, same era.
L. Caffarelli, L. Silvestre, An extension problem related to the fractional Laplacian. Comm. PDE
2007
Cited alongside, same era.
2014
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M. Maida, E. Maurel-Segala, Free transport-entropy inequalities for non-convex potentials and application to concentration for random matrices, Probab. Theory Relat. Fields
2014
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F. Bekerman, A. Figalli, A. Guionnet, Transport maps for Beta-matrix models and Universality, Comm. Math. Phys
2015
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X. Blanc, M. Lewin, The Crystallization Conjecture: A Review, EMS surveys
2015
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S. Kapfer and W. Krauth. Two-dimensional melting: From liquid-hexatic coexistence to continuous transitions. Physical review letters
2015
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2015
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F. Rassoul-Agha, T. Seppäläinen, A course on large deviation theory with an introduction to Gibbs measures, American Mathematical Society
2015
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S. Rota Nodari, S. Serfaty, Renormalized energy equidistribution and local charge balance in 2D Coulomb systems, Inter. Math. Research Notices
2015
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N. Rougerie, J. Yngvason, Incompressibility estimates for the Laughlin phase, Comm. Math. Phys
2015
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E. Sandier, S. Serfaty, 1D Log Gases and the Renormalized Energy: Crystallization at Vanishing Temperature, Proba. Theor. Rel. Fields,
2015
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S. Serfaty, Coulomb gases and Ginzburg-Landau vortices
2015
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2016
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D. S. Dean, P. Le Doussal, S. N. Majumdar, G. Schehr, Non-interacting fermions at finite temperature in a d-dimensional trap: universal correlations, Phys. Rev. A
2016
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T. Leblé, Logarithmic, Coulomb and Riesz energy of point processes, J. Stat. Phys,
2016
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T. Leblé, Local microscopic behavior for 2D Coulomb gases, Probab. Theory Relat. Fields
2016
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N. Rougerie, S. Serfaty, Higher Dimensional Coulomb Gases and Renormalized Energy Functionals, Comm. Pure Appl. Math
2016
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S. Torquato, Hyperuniformity and its Generalizations, Phys. Rev. E
2016
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H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, M. Viazovska, The sphere packing problem in dimension 24, Ann. of Math
2017
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T. Leblé, S. Serfaty, O. Zeitouni, Large deviations for the two-dimensional two-component plasma. Comm. Math. Phys
2017
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M. Petrache, S. Serfaty, Next Order Asymptotics and Renormalized Energy for Riesz Interactions, J. Inst. Math. Jussieu
2017
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M. Viazovska, The sphere packing problem in dimension 8, Ann. of Math
2017
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E. Sandier, S. Serfaty, 2D Coulomb Gases and the Renormalized Energy, Annals of Proba
2083
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