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Log Correlations and Random Matrices

Total Cost €


EC-Contrib. €






Project "LogCorRM" data sheet

The following table provides information about the project.


Organization address
city: OXFORD
postcode: OX1 2JD

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Total cost 1˙778˙516 €
 EC max contribution 1˙778˙516 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-ADG
 Funding Scheme ERC-ADG
 Starting year 2017
 Duration (year-month-day) from 2017-09-01   to  2022-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
2    UNIVERSITY OF BRISTOL UK (BRISTOL) participant 389˙637.00


 Project objective

Random Matrix Theory has been of central importance in Mathematical Physics for over 50 years. It has deep connections with many other areas of Mathematics and a remarkably wide range of applications. In 2012, a new avenue of research was initiated linking Random Matrix Theory to the highly active area of Probability Theory concerned with the extreme values of logarithmically correlated Gaussian fields, such as the branching random walk and the two-dimensional Gaussian Free Field. This connects the extreme value statistics of the characteristic polynomials of random matrices asymptotically to those of the Gaussian fields in question, allowing some important and long-standing open questions to be addressed for the first time. It has led to a flurry of activity and significant progress towards proving some of the main conjectures. A remarkable discovery has been that the characteristic polynomials of random matrices exhibit, asymptotically, a hierarchical branching/tree structure like that of the branching random walk. However, many of the most important questions remain open. My aim is to attack some of these problems using ideas and techniques that have so far not been applied to them: I believe it is possible to compute some important statistical quantities relating to the extreme values of characteristic polynomials exactly, for the first time, by establishing connections with integrable systems, representation theory, and enumerative combinatorics. Such connections have not previously been explored. I anticipate that this will have a significant impact on an area that is currently in a rapid phase of development and that it will settle some of the principal unresolved conjectures. I further believe that ideas exploiting the hierarchical branching structure may have new and unexpected implications for areas connected with Random Matrix Theory, including, in particular, Number Theory, and I plan to explore these too.


year authors and title journal last update
List of publications.
2019 Theodoros Assiotis
Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices
published pages: , ISSN: 1815-0659, DOI: 10.3842/SIGMA.2019.067
Symmetry, Integrability and Geometry: Methods and Applications 2020-04-03
2019 J P Keating, D J Smith
Twin prime correlations from the pair correlation of Riemann zeros
published pages: 365201, ISSN: 1751-8113, DOI: 10.1088/1751-8121/ab3521
Journal of Physics A: Mathematical and Theoretical 52/36 2020-04-03
2019 Theodoros Assiotis
On a gateway between the Laguerre process and dynamics on partitions
published pages: 1055, ISSN: 1980-0436, DOI: 10.30757/alea.v16-38
Latin American Journal of Probability and Mathematical Statistics 16/2 2020-04-03
2020 Theodoros Assiotis
Determinantal Structures in Space-Inhomogeneous Dynamics on Interlacing Arrays
published pages: 909-940, ISSN: 1424-0637, DOI: 10.1007/s00023-019-00881-5
Annales Henri Poincaré 21/3 2020-04-03
2019 Estelle Basor, Pavel Bleher, Robert Buckingham, Tamara Grava, Alexander Its, Elizabeth Its, Jonathan P Keating
A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions
published pages: 4033-4078, ISSN: 0951-7715, DOI: 10.1088/1361-6544/ab28c7
Nonlinearity 32/10 2020-04-03
2019 Edva Roditty-Gershon, Chris Hall, Jonathan P. Keating
Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in q[t]
published pages: 1-18, ISSN: 1793-0421, DOI: 10.1142/s1793042120500529
International Journal of Number Theory 2020-04-03
2018 Brian Conrey, Jonathan P. Keating
Moments of zeta and correlations of divisor‐sums: V
published pages: 729-752, ISSN: 0024-6115, DOI: 10.1112/plms.12196
Proceedings of the London Mathematical Society 118/4 2019-10-01
2019 E. C. Bailey, J. P. Keating
On the Moments of the Moments of the Characteristic Polynomials of Random Unitary Matrices
published pages: , ISSN: 0010-3616, DOI: 10.1007/s00220-019-03503-7
Communications in Mathematical Physics 2019-10-01
2019 Chris Hall, Jonathan P. Keating, Edva Roditty-Gershon
Variance of arithmetic sums and L-functions inq[t]
published pages: 19-92, ISSN: 1937-0652, DOI: 10.2140/ant.2019.13.19
Algebra & Number Theory 13/1 2019-09-17
2018 Yan V Fyodorov, Sven Gnutzmann, Jonathan P Keating
Extreme values of CUE characteristic polynomials: a numerical study
published pages: 464001, ISSN: 1751-8113, DOI: 10.1088/1751-8121/aae65a
Journal of Physics A: Mathematical and Theoretical 51/46 2019-09-17

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