Log Correlations and Random Matrices

Project Information

LogCorRM

Grant agreement ID: 740900

DOI

10.3030/740900

Project closed

EC signature date 10 April 2017

Start date 1 September 2017

End date 31 August 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 778 516,00

EU contribution

€ 1 778 516,00

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (37)

On the moments of the moments of ζ(1/2 + it)

Author(s): E.C. Bailey, J.P. Keating
Published in: Journal of Number Theory, 2021, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2020.12.008

On the distribution of equivalence classes of random symmetric <i>p</i>‐adic matrices

Author(s): Valeriya Kovaleva
Published in: Mathematika, Issue 5, 2023, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/mtk.12212

Moments of moments of the characteristic polynomials of random orthogonal and symplectic matrices

Author(s): Tom Claeys; Johannes Forkel; Jonathan P. Keating
Published in: Proceedings of the Royal Society of London A, Issue 3, 2023, ISSN 1471-2946
Publisher: The Royal Society
DOI: 10.1098/rspa.2022.0652

On the Joint Moments of the Characteristic Polynomials of Random Unitary Matrices

Author(s): Assiotis, T; Keating, JP; Warren, J
Published in: IMRN, Issue 30, 2021, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnab336

On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices

Author(s): Assiotis, T; Bailey, E; Keating, J
Published in: Annales de l'Institut Henri Poincaré D, Issue 4, 2022, ISSN 2308-5827
Publisher: European Mathematical Society
DOI: 10.4171/aihpd/127

Moments of generalized Cauchy random matrices and continuous-Hahn polynomials

Author(s): Theodoros Assiotis; Benjamin Bedert; Mustafa Alper Gunes; Arun Soor
Published in: Nonlinearity, Issue 8, 2021, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/abfeac

Magnitude and Holmes–Thompson intrinsic volumes of convex bodies

Author(s): Mark Meckes
Published in: Canadian Mathematical Bulletin, Issue 18, 2022, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008439522000728

Spaces of extremal magnitude

Author(s): Tom Leinster; Mark Meckes
Published in: Proceedings of the American Mathematical Society, Issue 14, 2023, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/16433

Type-I contributions to the one and two level densities of quadratic Dirichlet L–functions over function fields

Author(s): Hung M. Bui, Alexandra Florea, Jonathan P. Keating
Published in: Journal of Number Theory, Issue 221, 2021, Page(s) 389-423, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2020.10.021

On the Critical–Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective

Author(s): Jonathan P. Keating; Mo Dick Wong
Published in: Communications in Mathematical Physics, Issue 10, 2022, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-022-04429-3

Hierarchical structure in the trace formula*

Author(s): J P Keating
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 23, 2022, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ac82d6

Universal characteristics of deep neural network loss surfaces from random matrix theory

Author(s): Nicholas P Baskerville; Jonathan P Keating; Francesco Mezzadri; Joseph Najnudel; Diego Granziol
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 5, 2022, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/aca7f5

On a distinguished family of random variables and Painlev\'e equations

Author(s): Theodoros Assiotis; Benjamin Bedert; Mustafa Alper Gunes; Arun Soor
Published in: Probability and Mathematical Physics, Issue 3, 2021, ISSN 2690-0998
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/pmp.2021.2.613

A Spin Glass Model for the Loss Surfaces of Generative Adversarial Networks

Author(s): Nicholas P. Baskerville; Jonathan P. Keating; Francesco Mezzadri; Joseph Najnudel
Published in: Journal of Statistical Physics, Issue 6, 2022, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-022-02875-w

Infinite -adic random matrices and ergodic decomposition of -adic Hua measures

Author(s): Theodoros Assiotis
Published in: Transactions of the American Mathematical Society, Issue 4, 2022, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8526

The Ratios Conjecture and upper bounds for negative moments of -functions over function fields

Author(s): Bui, HM; Florea, A; Keating, J
Published in: Transactions of the American Mathematical Society, Issue 36, 2023, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8907

Tail universality of critical Gaussian multiplicative chaos

Author(s): Wong, Mo Dick
Published in: Probability Theory and Related Fields, Issue 1, 2020, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-020-00960-3

Extreme values of CUE characteristic polynomials: a numerical study

Author(s): Yan V Fyodorov, Sven Gnutzmann, Jonathan P Keating
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 51/46, 2018, Page(s) 464001, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/aae65a

Variance of arithmetic sums and L-functions in q[t]

Author(s): Chris Hall, Jonathan P. Keating, Edva Roditty-Gershon
Published in: Algebra & Number Theory, Issue 13/1, 2019, Page(s) 19-92, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/ant.2019.13.19

Moments of zeta and correlations of divisor‐sums: V

Author(s): Brian Conrey, Jonathan P. Keating
Published in: Proceedings of the London Mathematical Society, Issue 118/4, 2018, Page(s) 729-752, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12196

On the Moments of the Moments of the Characteristic Polynomials of Random Unitary Matrices

Author(s): E. C. Bailey, J. P. Keating
Published in: Communications in Mathematical Physics, 2019, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-019-03503-7

A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions

Author(s): Estelle Basor, Pavel Bleher, Robert Buckingham, Tamara Grava, Alexander Its, Elizabeth Its, Jonathan P Keating
Published in: Nonlinearity, Issue 32/10, 2019, Page(s) 4033-4078, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ab28c7

Twin prime correlations from the pair correlation of Riemann zeros

Author(s): J P Keating, D J Smith
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 52/36, 2019, Page(s) 365201, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ab3521

Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices

Author(s): Theodoros Assiotis
Published in: Symmetry, Integrability and Geometry: Methods and Applications, 2019, ISSN 1815-0659
Publisher: Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine
DOI: 10.3842/SIGMA.2019.067

On a gateway between the Laguerre process and dynamics on partitions

Author(s): Theodoros Assiotis
Published in: Latin American Journal of Probability and Mathematical Statistics, Issue 16/2, 2019, Page(s) 1055, ISSN 1980-0436
Publisher: Instituto Nacional de Matematica Pura e Aplicada
DOI: 10.30757/alea.v16-38

Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in q[t]

Author(s): Edva Roditty-Gershon, Chris Hall, Jonathan P. Keating
Published in: International Journal of Number Theory, 2019, Page(s) 1-18, ISSN 1793-0421
Publisher: World Scientific Publishing Co
DOI: 10.1142/s1793042120500529

Determinantal Structures in Space-Inhomogeneous Dynamics on Interlacing Arrays

Author(s): Theodoros Assiotis
Published in: Annales Henri Poincaré, Issue 21/3, 2020, Page(s) 909-940, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-019-00881-5

On the moments of characteristic polynomials

Author(s): Bhargavi Jonnadula; Jonathan P. Keating; Francesco Mezzadri
Published in: Glasgow Mathematical Journal, Issue 4, 2022, ISSN 0017-0895
Publisher: Cambridge University Press
DOI: 10.1017/s0017089522000258

Symmetric Function Theory and Unitary Invariant Ensembles

Author(s): Bhargavi Jonnadula; Jon P Keating; Francesco Mezzadri
Published in: Journal of Mathematical Physics, Issue 2, 2021, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0048364

Moments of quadratic twists of elliptic curveL-functions over function fields

Author(s): Hung M. Bui, Alexandra Florea, Jonathan P. Keating, Edva Roditty-Gershon
Published in: Algebra & Number Theory, Issue 14/7, 2020, Page(s) 1853-1893, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/ant.2020.14.1853

The classical compact groups and Gaussian multiplicative chaos

Author(s): Johannes Forkel; Jon P Keating
Published in: Nonlinearity, Issue 5, 2021, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ac1164

Appearance of Random Matrix Theory in deep learning

Author(s): Nicholas P. Baskerville; Diego Granziol; Jonathan P. Keating
Published in: Physica A: Statistical Mechanics and its Applications, Issue 6, 2022, ISSN 0378-4371
Publisher: Elsevier BV
DOI: 10.1016/j.physa.2021.126742

Maxima of log-correlated fields: some recent developments*

Author(s): E C Bailey; J P Keating
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 1, 2022, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ac4394

Multifractal Eigenfunctions for a Singular Quantum Billiard

Author(s): Jon P Keating; Henrik Ueberschär
Published in: https://hal.sorbonne-universite.fr/hal-03460902, Issue 24, 2022, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-021-04214-8

The boundary of the orbital beta process

Author(s): Theodoros Assiotis; Joseph Najnudel
Published in: Moscow Mathematical Journal, Issue 7, 2021, ISSN 1609-4514
Publisher: Independent University of Moscow
DOI: 10.17323/1609-4514-2021-21-4-659-694

Moments of moments of characteristic polynomials of random unitary matrices and lattice point counts

Author(s): Theodoros Assiotis, Jonathan P. Keating
Published in: Random Matrices: Theory and Applications, 2020, Page(s) 2150019, ISSN 2010-3263
Publisher: World Scientific
DOI: 10.1142/s2010326321500192

Moments of Moments and Branching Random Walks

Author(s): E. C. Bailey, J. P. Keating
Published in: Journal of Statistical Physics, Issue 182/1, 2021, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-020-02696-9

Other (11)

The Eigenvalues of Random Matrices

Author(s): Meckes, Elizabeth
Published in: ArXiv, Issue 35, 2020
Publisher: ArXiv
DOI: 10.48550/arxiv.2101.02928

Joint moments of higher order derivatives of CUE characteristic polynomials I: asymptotic formulae

Author(s): Keating, Jonathan P.; Wei, Fei
Published in: ArXiv, Issue 4, 2023
Publisher: ArXiv
DOI: 10.48550/arxiv.2307.01625

Winding and intersection of Brownian motions

Author(s): Sauzedde, Isao
Published in: ArXiv, Issue 3, 2021
Publisher: ArXiv
DOI: 10.48550/arxiv.2112.01645

Convergence of the logarithm of the characteristic polynomial of unitary Brownian motion in Sobolev space

Author(s): Forkel, Johannes; Sauzedde, Isao
Published in: ArXiv, Issue 14, 2022
Publisher: ArXiv
DOI: 10.48550/arxiv.2211.02034

LECTURE HALL GRAPHS AND THE ASKEY SCHEME

Author(s): SYLVIE CORTEEL, BHARGAVI JONNADULA, JONATHAN P. KEATING, AND JANG SOO KIM
Published in: 2023
Publisher: ArXiv

Homotopy and holonomy of the planar Brownian motion in a Poisson punctured plane

Author(s): Sauzedde, Isao
Published in: ArXiv, Issue 1, 2021
Publisher: ArXiv
DOI: 10.48550/arxiv.2110.15816

Brownian windings, Stochastic Green's formula and inhomogeneous magnetic impurities

Author(s): Sauzedde, Isao
Published in: ArXiv, Issue 2, 2023
Publisher: ArXiv
DOI: 10.48550/arxiv.2301.00551

Maximum Absolute Determinants of Upper Hessenberg Bohemian Matrices

Author(s): Keating, Jonathan P.; Kele��, Ahmet Abdullah
Published in: ArXiv, Issue 21, 2020
Publisher: ArXiv
DOI: 10.48550/arxiv.2003.00454

Joint moments of higher order derivatives of CUE characteristic polynomials II: Structures, recursive relations, and applications

Author(s): Keating, Jonathan P.; Wei, Fei
Published in: ArXiv, Issue 5, 2023
Publisher: ArXiv
DOI: 10.48550/arxiv.2307.02831

Equidistribution of high traces of random matrices over finite fields and cancellation in character sums of high conductor

Author(s): Gorodetsky, Ofir; Kovaleva, Valeriya
Published in: ArXiv, Issue 14, 2023
Publisher: ArXiv
DOI: 10.48550/arxiv.2307.01344

Multifractal eigenfunctions for quantum star graphs

Author(s): Keating, Jonathan P.; Ueberschaer, Henrik
Published in: Issue 25, 2022
Publisher: ArXiv
DOI: 10.48550/arxiv.2202.13634