Random matrices, universality and disordered quantum systems
Project Period: 2014-03-01 – 2019-08-31
Externally Funded
Acronym
RANMAT
Principal Investigator
László Erdös
Department(s)
Erdoes Group
Grant Number
338804
Funding Organisation
EC/FP7
50 Publications
2016 | Journal Article | IST-REx-ID: 1157 |

Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population
J. Lee, K. Schnelli, Annals of Applied Probability 26 (2016) 3786–3839.
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J. Lee, K. Schnelli, Annals of Applied Probability 26 (2016) 3786–3839.
2016 | Journal Article | IST-REx-ID: 1219 |

Bulk universality for deformed wigner matrices
J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016) 2349–2425.
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J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016) 2349–2425.
2016 | Journal Article | IST-REx-ID: 1280 |

Fixed energy universality for generalized wigner matrices
P. Bourgade, L. Erdös, H. Yau, J. Yin, Communications on Pure and Applied Mathematics 69 (2016) 1815–1881.
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P. Bourgade, L. Erdös, H. Yau, J. Yin, Communications on Pure and Applied Mathematics 69 (2016) 1815–1881.
2016 | Journal Article | IST-REx-ID: 1434 |

Local stability of the free additive convolution
Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016) 672–719.
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Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016) 672–719.
2016 | Journal Article | IST-REx-ID: 1489 |

Local spectral statistics of Gaussian matrices with correlated entries
O.H. Ajanki, L. Erdös, T.H. Krüger, Journal of Statistical Physics 163 (2016) 280–302.
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O.H. Ajanki, L. Erdös, T.H. Krüger, Journal of Statistical Physics 163 (2016) 280–302.
2014 | Conference Paper | IST-REx-ID: 1507 |

Random matrices, log-gases and Hölder regularity
L. Erdös, in:, Kyung Moon SA Co. Ltd., 2014, pp. 214–236.
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L. Erdös, in:, Kyung Moon SA Co. Ltd., 2014, pp. 214–236.
2015 | Journal Article | IST-REx-ID: 1864 |

The Altshuler–Shklovskii formulas for random band matrices II: The general case
L. Erdös, A. Knowles, Annales Henri Poincare 16 (2015) 709–799.
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L. Erdös, A. Knowles, Annales Henri Poincare 16 (2015) 709–799.
2016 | Journal Article | IST-REx-ID: 1881 |

Extremal eigenvalues and eigenvectors of deformed Wigner matrices
J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 165–241.
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J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 165–241.
2014 | Journal Article | IST-REx-ID: 2019 |

Phase transition in the density of states of quantum spin glasses
L. Erdös, D.J. Schröder, Mathematical Physics, Analysis and Geometry 17 (2014) 441–464.
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L. Erdös, D.J. Schröder, Mathematical Physics, Analysis and Geometry 17 (2014) 441–464.
2014 | Journal Article | IST-REx-ID: 2225 |

Isotropic local laws for sample covariance and generalized Wigner matrices
A. Bloemendal, L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 19 (2014).
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A. Bloemendal, L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 19 (2014).
2017 | Journal Article | IST-REx-ID: 447 |

Fluctuations of the competition interface in presence of shocks
P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística 9 (2017) 299–325.
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P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística 9 (2017) 299–325.
2017 | Journal Article | IST-REx-ID: 483 |

Universality for a class of random band matrices
P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.
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P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.
2017 | Book | IST-REx-ID: 567
A Dynamical Approach to Random Matrix Theory
L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017.
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L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017.
2017 | Journal Article | IST-REx-ID: 615 |

Universality for random matrix flows with time dependent density
L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability and Statistics 53 (2017) 1606–1656.
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L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability and Statistics 53 (2017) 1606–1656.
2018 | Journal Article | IST-REx-ID: 690 |

Local law and Tracy–Widom limit for sparse random matrices
J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).
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J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).
2017 | Journal Article | IST-REx-ID: 721 |

Singularities of solutions to quadratic vector equations on the complex upper half plane
O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics 70 (2017) 1672–1705.
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O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics 70 (2017) 1672–1705.
2019 | Conference Paper | IST-REx-ID: 8175 |

New edge asymptotics of skew Young diagrams via free boundaries
D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.
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D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.
2018 | Journal Article | IST-REx-ID: 556 |

The free boundary Schur process and applications I
D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.
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D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.
2021 | Journal Article | IST-REx-ID: 9550 |

Equipartition principle for Wigner matrices
Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
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Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).
2021 | Journal Article | IST-REx-ID: 9912 |

Scattering in quantum dots via noncommutative rational functions
L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.
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L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.
2021 | Journal Article | IST-REx-ID: 10405 |

Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices
G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics (2021).
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G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics (2021).
2020 | Journal Article | IST-REx-ID: 7512 |

Local laws for polynomials of Wigner matrices
L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).
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L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).
2020 | Journal Article | IST-REx-ID: 8601 |

Edge universality for non-Hermitian random matrices
G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2020).
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G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2020).
2020 | Journal Article | IST-REx-ID: 9104 |

On the support of the free additive convolution
Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.
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Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.
2020 | Journal Article | IST-REx-ID: 10862 |

Spectral rigidity for addition of random matrices at the regular edge
Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).
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Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).
2019 | Journal Article | IST-REx-ID: 72 |

Limit law of a second class particle in TASEP with non-random initial condition
P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.
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P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.
2019 | Journal Article | IST-REx-ID: 429 |

Stability of the matrix Dyson equation and random matrices with correlations
O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.
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O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.
2020 | Journal Article | IST-REx-ID: 6488 |

Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices
G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).
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G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).
2019 | Journal Article | IST-REx-ID: 6511 |

Local single ring theorem on optimal scale
Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.
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Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.
2017 | Journal Article | IST-REx-ID: 550 |

Singularities of the density of states of random Gram matrices
J. Alt, Electronic Communications in Probability 22 (2017).
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J. Alt, Electronic Communications in Probability 22 (2017).
2019 | Journal Article | IST-REx-ID: 6240 |

Location of the spectrum of Kronecker random matrices
J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.
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J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.
2015 | Journal Article | IST-REx-ID: 1677 |

The local semicircle law for random matrices with a fourfold symmetry
J. Alt, Journal of Mathematical Physics 56 (2015).
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J. Alt, Journal of Mathematical Physics 56 (2015).
2020 | Journal Article | IST-REx-ID: 6185 |

Cusp universality for random matrices I: Local law and the complex Hermitian case
L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.
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L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.
2019 | Journal Article | IST-REx-ID: 6182 |

Random matrices with slow correlation decay
L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).
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| arXiv
L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).
2017 | Journal Article | IST-REx-ID: 1144 |

Fluctuations of functions of Wigner matrices
L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017).
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L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017).
2019 | Journal Article | IST-REx-ID: 6186 |

Cusp universality for random matrices, II: The real symmetric case
G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.
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G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.
2021 | Thesis | IST-REx-ID: 9022 |

Fluctuations in the spectrum of random matrices
G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.
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G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.
2018 | Journal Article | IST-REx-ID: 566 |

Local inhomogeneous circular law
J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.
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J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.
2018 | Journal Article | IST-REx-ID: 181 |

Power law decay for systems of randomly coupled differential equations
L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.
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L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.
2018 | Journal Article | IST-REx-ID: 70 |

Transition to shocks in TASEP and decoupling of last passage times
P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.
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P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.
2018 | Journal Article | IST-REx-ID: 5971 |

Bounds on the norm of Wigner-type random matrices
L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).
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L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).
2020 | Journal Article | IST-REx-ID: 6184 |

Correlated random matrices: Band rigidity and edge universality
J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.
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J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.
2017 | Journal Article | IST-REx-ID: 1528 |

Delocalization for a class of random block band matrices
Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.
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Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.
2017 | Journal Article | IST-REx-ID: 1337 |

Universality for general Wigner-type matrices
O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 169 (2017) 667–727.
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O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 169 (2017) 667–727.
2017 | Journal Article | IST-REx-ID: 1207 |

Local law of addition of random matrices on optimal scale
Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990.
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Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990.
2019 | Thesis | IST-REx-ID: 6179 |

From Dyson to Pearcey: Universal statistics in random matrix theory
D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.
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D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.
2018 | Journal Article | IST-REx-ID: 1012 |

Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues
L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.
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L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.
2018 | Thesis | IST-REx-ID: 149 |

Dyson equation and eigenvalue statistics of random matrices
J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018.
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J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018.
2017 | Journal Article | IST-REx-ID: 1010 |

Local law for random Gram matrices
J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).
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| WoS
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J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).
2017 | Journal Article | IST-REx-ID: 733 |

Convergence rate for spectral distribution of addition of random matrices
Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.
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Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.