Large deviations from the circular law
ESAIM: PS, 2 (1998) 123-134
Published online: 2002-08-15
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Persistence and ball exponents for Gaussian stationary processes
Naomi D. Feldheim, Ohad N. Feldheim and Sumit MukherjeeCommunications on Pure and Applied Mathematics (2025)
https://doi.org/10.1002/cpa.22255
On the maximum of the potential of a general two-dimensional Coulomb gas
Luke PeilenElectronic Communications in Probability 30 (none) (2025)
https://doi.org/10.1214/25-ECP692
Large deviations principles for Coulomb gases at intermediate temperature regime
David Padilla-GarzaElectronic Journal of Probability 29 (none) (2024)
https://doi.org/10.1214/24-EJP1255
Quenched complexity of equilibria for asymmetric generalized Lotka–Volterra equations
Valentina Ros, Felix Roy, Giulio Biroli and Guy BuninJournal of Physics A: Mathematical and Theoretical 56 (30) 305003 (2023)
https://doi.org/10.1088/1751-8121/ace00f
General truncated linear statistics for the top eigenvalues of random matrices
Aurélien GrabschJournal of Physics A: Mathematical and Theoretical 55 (12) 124001 (2022)
https://doi.org/10.1088/1751-8121/ac52e3
Statistical limits of dictionary learning: Random matrix theory and the spectral replica method
Jean Barbier and Nicolas MacrisPhysical Review E 106 (2) (2022)
https://doi.org/10.1103/PhysRevE.106.024136
Large deviation principles via spherical integrals
Serban Belinschi, Alice Guionnet and Jiaoyang HuangProbability and Mathematical Physics 3 (3) 543 (2022)
https://doi.org/10.2140/pmp.2022.3.543
Precise Deviations for Disk Counting Statistics of Invariant Determinantal Processes
Marcel Fenzl and Gaultier LambertInternational Mathematics Research Notices 2022 (10) 7420 (2022)
https://doi.org/10.1093/imrn/rnaa341
Counting equilibria of large complex systems by instability index
Gérard Ben Arous, Yan V. Fyodorov and Boris A. KhoruzhenkoProceedings of the National Academy of Sciences 118 (34) (2021)
https://doi.org/10.1073/pnas.2023719118
Large deviations for configurations generated by Gibbs distributions with energy functionals consisting of singular interaction and weakly confining potentials
Paul Dupuis, Vaios Laschos and Kavita RamananElectronic Journal of Probability 25 (none) (2020)
https://doi.org/10.1214/20-EJP449
Maximum of the Characteristic Polynomial of the Ginibre Ensemble
Gaultier LambertCommunications in Mathematical Physics 378 (2) 943 (2020)
https://doi.org/10.1007/s00220-020-03813-1
Ground states and hyperuniformity of the hierarchical Coulomb gas in all dimensions
Shirshendu Ganguly and Sourav SarkarProbability Theory and Related Fields 177 (3-4) 621 (2020)
https://doi.org/10.1007/s00440-019-00955-9
Gaussian Complex Zeros on the Hole Event: The Emergence of a Forbidden Region
Subhroshekhar Ghosh and Alon NishryCommunications on Pure and Applied Mathematics 72 (1) 3 (2019)
https://doi.org/10.1002/cpa.21800
Rigidity of the three-dimensional hierarchical Coulomb gas
Sourav ChatterjeeProbability Theory and Related Fields 175 (3-4) 1123 (2019)
https://doi.org/10.1007/s00440-019-00912-6
A large deviation principle for empirical measures on Polish spaces: Application to singular Gibbs measures on manifolds
David García-ZeladaAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques 55 (3) (2019)
https://doi.org/10.1214/18-AIHP922
On Large Deviations for Gibbs Measures, Mean Energy and Gamma-Convergence
Robert J. BermanConstructive Approximation 48 (1) 3 (2018)
https://doi.org/10.1007/s00365-018-9437-3
The largest root of random Kac polynomials is heavy tailed
Raphaël ButezElectronic Communications in Probability 23 (none) (2018)
https://doi.org/10.1214/18-ECP114
Point Processes, Hole Events, and Large Deviations: Random Complex Zeros and Coulomb Gases
Subhroshekhar Ghosh and Alon NishryConstructive Approximation 48 (1) 101 (2018)
https://doi.org/10.1007/s00365-018-9418-6
Equidistribution of Jellium Energy for Coulomb and Riesz Interactions
Mircea Petrache and Simona Rota NodariConstructive Approximation 47 (1) 163 (2018)
https://doi.org/10.1007/s00365-017-9395-1
Large Deviations for Gibbs Measures with Singular Hamiltonians and Emergence of Kähler–Einstein Metrics
Robert J. BermanCommunications in Mathematical Physics 354 (3) 1133 (2017)
https://doi.org/10.1007/s00220-017-2926-6
Large deviations for biorthogonal ensembles and variational formulation for the Dykema-Haagerup distribution
Raphaël ButezElectronic Communications in Probability 22 (none) (2017)
https://doi.org/10.1214/17-ECP68
Local microscopic behavior for 2D Coulomb gases
Thomas LebléProbability Theory and Related Fields 169 (3-4) 931 (2017)
https://doi.org/10.1007/s00440-016-0744-y
Local Density for Two-Dimensional One-Component Plasma
Roland Bauerschmidt, Paul Bourgade, Miika Nikula and Horng-Tzer YauCommunications in Mathematical Physics (2017)
https://doi.org/10.1007/s00220-017-2932-8
Universal large deviations for Kac polynomials
Raphaël Butez and Ofer ZeitouniElectronic Communications in Probability 22 (none) (2017)
https://doi.org/10.1214/16-ECP33
Tridiagonal Random Matrix: Gaussian Fluctuations and Deviations
Deng ZhangJournal of Theoretical Probability 30 (3) 1076 (2017)
https://doi.org/10.1007/s10959-016-0683-7
Large deviation principle for empirical fields of Log and Riesz gases
Thomas Leblé and Sylvia SerfatyInventiones mathematicae 210 (3) 645 (2017)
https://doi.org/10.1007/s00222-017-0738-0
Large Deviations for the Two-Dimensional Two-Component Plasma
Thomas Leblé, Sylvia Serfaty and Ofer ZeitouniCommunications in Mathematical Physics 350 (1) 301 (2017)
https://doi.org/10.1007/s00220-016-2735-3
Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices
Aurélien Grabsch, Satya N. Majumdar and Christophe TexierJournal of Statistical Physics 167 (2) 234 (2017)
https://doi.org/10.1007/s10955-017-1755-5
The Real Ginibre Ensemble with $$k=O(n)$$ k = O ( n ) Real Eigenvalues
Luis Carlos García del Molino, Khashayar Pakdaman, Jonathan Touboul and Gilles WainribJournal of Statistical Physics 163 (2) 303 (2016)
https://doi.org/10.1007/s10955-016-1485-0
Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals
Nicolas Rougerie and Sylvia SerfatyCommunications on Pure and Applied Mathematics 69 (3) 519 (2016)
https://doi.org/10.1002/cpa.21570
What is the probability that a large random matrix has no real eigenvalues?
Eugene Kanzieper, Mihail Poplavskyi, Carsten Timm, Roger Tribe and Oleg ZaboronskiThe Annals of Applied Probability 26 (5) (2016)
https://doi.org/10.1214/15-AAP1160
From Boltzmann to random matrices and beyond
Djalil ChafaïAnnales de la Faculté des sciences de Toulouse : Mathématiques 24 (4) 641 (2016)
https://doi.org/10.5802/afst.1459
Large deviations for the empirical measure of random polynomials: revisit of the Zeitouni-Zelditch theorem
Raphaël ButezElectronic Journal of Probability 21 (none) (2016)
https://doi.org/10.1214/16-EJP5
Large Deviations for Zeros of Random Polynomials with i.i.d. Exponential Coefficients
Subhroshekhar Ghosh and Ofer ZeitouniInternational Mathematics Research Notices 2016 (5) 1308 (2016)
https://doi.org/10.1093/imrn/rnv174
Large-NAsymptotic Expansion for Mean Field Models with Coulomb Gas Interaction
Gaëtan Borot, Alice Guionnet and Karol K. KozlowskiInternational Mathematics Research Notices 2015 (20) 10451 (2015)
https://doi.org/10.1093/imrn/rnu260
The heterogeneous gas with singular interaction: generalized circular law and heterogeneous renormalized energy
Luis Carlos García del Molino, Khashayar Pakdaman and Jonathan TouboulJournal of Physics A: Mathematical and Theoretical 48 (4) 045208 (2015)
https://doi.org/10.1088/1751-8113/48/4/045208
2D Coulomb gases and the renormalized energy
Etienne Sandier and Sylvia SerfatyThe Annals of Probability 43 (4) (2015)
https://doi.org/10.1214/14-AOP927
Circular law for random matrices with unconditional log-concave distribution
Radosław Adamczak and Djalil ChafaïCommunications in Contemporary Mathematics 17 (04) 1550020 (2015)
https://doi.org/10.1142/S0219199715500200
Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition
Fabio Deelan Cunden, Anna Maltsev and Francesco MezzadriPhysical Review E 91 (6) (2015)
https://doi.org/10.1103/PhysRevE.91.060105
Index distribution of the Ginibre ensemble
Romain Allez, Jonathan Touboul and Gilles WainribJournal of Physics A: Mathematical and Theoretical 47 (4) 042001 (2014)
https://doi.org/10.1088/1751-8113/47/4/042001
Determinantal Point Processes and Fermions on Complex Manifolds: Large Deviations and Bosonization
Robert J. BermanCommunications in Mathematical Physics 327 (1) 1 (2014)
https://doi.org/10.1007/s00220-014-1891-6
A Note on the Second Order Universality at the Edge of Coulomb Gases on the Plane
Djalil Chafaï and Sandrine PéchéJournal of Statistical Physics 156 (2) 368 (2014)
https://doi.org/10.1007/s10955-014-1007-x
Quantum Hall Phases and Plasma Analogy in Rotating Trapped Bose Gases
N. Rougerie, S. Serfaty and J. YngvasonJournal of Statistical Physics 154 (1-2) 2 (2014)
https://doi.org/10.1007/s10955-013-0766-0
First-order global asymptotics for confined particles with singular pair repulsion
Djalil Chafaï, Nathael Gozlan and Pierre-André ZittThe Annals of Applied Probability 24 (6) (2014)
https://doi.org/10.1214/13-AAP980
Systems with Coulomb interactions
Sylvia SerfatyJournées équations aux dérivées partielles 1 (2014)
https://doi.org/10.5802/jedp.112
Remarks on a Constrained Optimization Problem for the Ginibre Ensemble
Scott N. Armstrong, Sylvia Serfaty and Ofer ZeitouniPotential Analysis 41 (3) 945 (2014)
https://doi.org/10.1007/s11118-014-9402-0
Ginzburg-Landau Vortices, Coulomb Gases, and Renormalized Energies
Sylvia SerfatyJournal of Statistical Physics 154 (3) 660 (2014)
https://doi.org/10.1007/s10955-013-0891-9
LARGE DEVIATIONS FOR A NON-CENTERED WISHART MATRIX
ADRIEN HARDY and ARNO B. J. KUIJLAARSRandom Matrices: Theory and Applications 02 (01) 1250016 (2013)
https://doi.org/10.1142/S2010326312500165
A solvable mixed charge ensemble on the line: global results
Brian Rider, Christopher D. Sinclair and Yuan XuProbability Theory and Related Fields 155 (1-2) 127 (2013)
https://doi.org/10.1007/s00440-011-0394-z
Large deviations and linear statistics for potential theoretic ensembles associated with regular closed sets
Maxim L. YattselevProbability Theory and Related Fields 156 (3-4) 827 (2013)
https://doi.org/10.1007/s00440-012-0444-1
Around the circular law
Charles Bordenave and Djalil ChafaïProbability Surveys 9 (none) (2012)
https://doi.org/10.1214/11-PS183
RANDOM RIGHT EIGENVALUES OF GAUSSIAN QUATERNIONIC MATRICES
FLORENT BENAYCH-GEORGES and FRANÇOIS CHAPONRandom Matrices: Theory and Applications 01 (02) 1150009 (2012)
https://doi.org/10.1142/S2010326311500092
Voiculescu’s Entropy and Potential Theory
Thomas BloomAnnales de la Faculté des sciences de Toulouse : Mathématiques 20 (S2) 57 (2011)
https://doi.org/10.5802/afst.1305
Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices
Dénes Petz and Júlia RéffyProbability Theory and Related Fields 133 (2) 175 (2005)
https://doi.org/10.1007/s00440-004-0420-5
Large deviations and stochastic calculus for large random matrices
Alice GuionnetProbability Surveys 1 (none) (2004)
https://doi.org/10.1214/154957804100000033
Discussions around Voiculescu's free entropies
Thierry Cabanal-Duvillard and Alice GuionnetAdvances in Mathematics 174 (2) 167 (2003)
https://doi.org/10.1016/S0001-8708(02)00032-4
Large Deviations Upper Bounds for the Laws of Matrix-Valued Processes and Non-Communicative Entropies
T. Cabanal Duvillard and A. GuionnetThe Annals of Probability 29 (3) (2001)
https://doi.org/10.1214/aop/1015345602