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IntRanSt SIGNED

Integrable Random Structures

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EC-Contrib. €

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Project "IntRanSt" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN 

Organization address
address: BELFIELD
city: DUBLIN
postcode: 4
website: www.ucd.ie

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 Ireland [IE]
 Project website http://www.maths.ucd.ie/
 Total cost 1˙579˙298 €
 EC max contribution 1˙579˙298 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-ADG
 Funding Scheme ERC-ADG
 Starting year 2015
 Duration (year-month-day) from 2015-10-01   to  2021-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN IE (DUBLIN) coordinator 1˙287˙861.00
2    UNIVERSITY OF BRISTOL UK (BRISTOL) participant 175˙061.00
3    THE UNIVERSITY OF WARWICK UK (COVENTRY) participant 116˙376.00

Map

 Project objective

The last few years have seen significant advances in the discovery and development of integrable models in probability, especially in the context of random polymers and the Kardar-Parisi-Zhang (KPZ) equation. Among these are the semi-discrete (O'Connell-Yor) and log-gamma (Seppalainen) random polymer models. Both of these models can be understood via a remarkable connection between the geometric RSK correspondence (a geometric lifting, or de-tropicalization, of the classical RSK correspondence) and the quantum Toda lattice, the eigenfunctions of which are known as Whittaker functions. This connection was discovered by the PI and further developed in collaboration with Corwin, Seppalainen and Zygouras. In particular, we have recently introduced a powerful combinatorial framework which underpins this connection. I have also explored this connection from an integrable systems point of view, revealing a very precise relation between classical, quantum and stochastic integrability in the context of the Toda lattice and some other integrable systems. The main objectives of this proposal are (1) to further develop the combinatorial framework in several directions which, in particular, will yield a wider family of integrable models, (2) to clarify and extend the relation between classical, quantum and stochastic integrability to a wider setting, and (3) to study thermodynamic and KPZ scaling limits of Whittaker functions (and associated measures) and their applications. The proposed research, which lies at the interface of probability, integrable systems, random matrices, statistical physics, automorphic forms, algebraic combinatorics and representation theory, will make novel contributions in all of these areas.

 Publications

year authors and title journal last update
List of publications.
2019 Fabio Deelan Cunden, Francesco Mezzadri, Neil O’Connell, Nick Simm
Moments of Random Matrices and Hypergeometric Orthogonal Polynomials
published pages: , ISSN: 0010-3616, DOI: 10.1007/s00220-019-03323-9
Communications in Mathematical Physics 2019-07-04
2018 Fabio Deelan Cunden, Antoine Dahlqvist, Neil O\'Connell
Integer moments of complex Wishart matrices and Hurwitz numbers
published pages: , ISSN: , DOI:
arXiv 2019-07-04
2018 Fabio Deelan Cunden, Francesco Mezzadri, Neil O’Connell
Free Fermions and the Classical Compact Groups
published pages: 768-801, ISSN: 0022-4715, DOI: 10.1007/s10955-018-2029-6
Journal of Statistical Physics 171/5 2019-07-04
2018 Assiotis, Theodoros; O\'Connell, Neil; Warren, Jon
Interlacing Diffusions
published pages: , ISSN: , DOI:
5 2019-07-04
2018 Benson Au, Guillaume Cébron, Antoine Dahlqvist, Franck Gabriel, Camille Male
Large permutation invariant random matrices are asymptotically free over the diagonal
published pages: , ISSN: , DOI:
arXiv 2019-07-04
2019 Jonas Arista, Neil O\'Connell
Loop-erased walks and random matrices
published pages: , ISSN: , DOI:
arXiv 2019-04-18
2017 Fabio Deelan Cunden, Paolo Facchi, Marilena Ligabò, Pierpaolo Vivo
Universality of the third-order phase transition in the constrained Coulomb gas
published pages: 53303, ISSN: 1742-5468, DOI: 10.1088/1742-5468/aa690c
Journal of Statistical Mechanics: Theory and Experiment 2017/5 2019-04-15
2018 Fabio Deelan Cunden, Paolo Facchi, Marilena Ligabò, Pierpaolo Vivo
Universality of the weak pushed-to-pulled transition in systems with repulsive interactions
published pages: 35LT01, ISSN: 1751-8113, DOI: 10.1088/1751-8121/aad147
Journal of Physics A: Mathematical and Theoretical 51/35 2019-04-15
2018 Fabio Deelan Cunden, Paolo Facchi, Marilena Ligabò, Pierpaolo Vivo
Third-order phase transition: random matrices and screened Coulomb gas with hard walls
published pages: , ISSN: , DOI:
arXiv 2019-04-15
2018 Fabio Deelan Cunden, Satya N. Majumdar, Neil O\'Connell
Free fermions and α-determinantal processes
published pages: , ISSN: , DOI:
arXiv 2019-04-15

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