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SPECTRUM SIGNED

Spectral theory of random operators

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EC-Contrib. €

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Partnership

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Project "SPECTRUM" data sheet

The following table provides information about the project.

Coordinator
QUEEN MARY UNIVERSITY OF LONDON 

Organization address
address: 327 MILE END ROAD
city: LONDON
postcode: E1 4NS
website: http://www.qmul.ac.uk

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 991˙750 €
 EC max contribution 991˙750 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-STG
 Funding Scheme ERC-STG
 Starting year 2015
 Duration (year-month-day) from 2015-06-01   to  2020-05-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    QUEEN MARY UNIVERSITY OF LONDON UK (LONDON) coordinator 824˙853.00
2    TEL AVIV UNIVERSITY IL (TEL AVIV) participant 166˙896.00

Map

 Project objective

The theme of this proposal is the study of random operators associated with some geometric structure, and the influence of the geometry on the spectral properties of the operator. Such operators appear in problems from theoretical physics, and lead to new and interesting mathematical structures. One circle of questions is related to random operators, which describe the motion of a quantum particle in a disordered medium, such as random band matrices. The behaviour of the particle is influenced by the underlying geometry, as quantified by the (non-rigorous) Thouless criterion for localisation in terms of the mixing time of the classical random walk; in the context of random band matrices, the predictions of the Thouless criterion are supported by additional (non-rigorous) arguments. These predictions have so far not been rigorously justified; an exception is my own result, validating it at the spectral edges. One of our goals is to develop new methods, which would be applicable in the bulk of the spectrum, for random band matrices and other operators with geometric structure. Another circle of questions is given by random processes taking values in large random matrices. The spectral properties of the random matrix at every point of the underlying space are described by the random matrix theory; but how does the spectrum evolve along the underlying space? The richness of this question is apparent from the one-dimensional case of Dyson Brownian motion. We intend to study the local eigenvalue statistics of general matrix-valued random processes with multi-dimensional underlying space; to give a complete description of the random processes which appear in the limit, first for the spectral edges and then for the bulk of the spectrum, and to explore the appearance of these processes in a variety of basic questions of mathematical physics.

 Publications

year authors and title journal last update
List of publications.
2018 Offer Kopelevitch
A Convergent $$varvec{frac{1}{N}}$$ 1 N Expansion for GUE
published pages: 3883-3899, ISSN: 1424-0637, DOI: 10.1007/s00023-018-0727-x
Annales Henri Poincaré 19/12 2019-11-11
2018 Alexander Magazinov
On Percolation of Two-Dimensional Hard Disks
published pages: 1-43, ISSN: 0010-3616, DOI: 10.1007/s00220-018-3193-x
Communications in Mathematical Physics 364/1 2019-11-11
2019 Martin Gebert
A lower Wegner estimate and bounds on the spectral shift function for continuum random Schrödinger operators
published pages: 108284, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2019.108284
Journal of Functional Analysis 277/11 2019-11-11
2018 Ilya Goldsheid, Sasha Sodin
Real eigenvalues in the non-Hermitian Anderson model
published pages: 3075-3093, ISSN: 1050-5164, DOI: 10.1214/18-AAP1383
The Annals of Applied Probability 28/5 2019-11-11
2018 VADIM GORIN, SASHA SODIN
The KPZ Equation and Moments of Random Matrices
published pages: 286-296, ISSN: 1812-9471, DOI: 10.15407/mag14.03.286
Zurnal matematiceskoj fiziki, analiza, geometrii 14/3 2019-11-11
2018 Yuri Kifer, Sasha Sodin
Nonconventional random matrix products
published pages: , ISSN: 1083-589X, DOI: 10.1214/18-ECP140
Electronic Communications in Probability 23 2019-11-11
2019 Emilio Fedele, Martin Gebert
On determinants identity minus Hankel matrix
published pages: 751-764, ISSN: 0024-6093, DOI: 10.1112/blms.12271
Bulletin of the London Mathematical Society 51/4 2019-11-11
2017 Sasha Sodin
Fluctuations of Interlacing Sequences
published pages: 364-401, ISSN: 1812-9471, DOI: 10.15407/mag13.04.364
Zurnal matematiceskoj fiziki, analiza, geometrii 13/4 2019-05-28
2017 Michael Aizenman, Ron Peled, Jeffrey Schenker, Mira Shamis, Sasha Sodin
Matrix regularizing effects of Gaussian perturbations
published pages: 1750028, ISSN: 0219-1997, DOI: 10.1142/S0219199717500286
Communications in Contemporary Mathematics 19/03 2019-05-28
2017 Sasha Sodin
ON THE CRITICAL POINTS OF RANDOM MATRIX CHARACTERISTIC POLYNOMIALS AND OF THE RIEMANN ξ-FUNCTION
published pages: 1-28, ISSN: 0033-5606, DOI: 10.1093/qmath/hax033
The Quarterly Journal of Mathematics 2019-05-28
2017 Ron Peled, Jeffrey Schenker, Mira Shamis, Sasha Sodin
On the Wegner Orbital Model
published pages: , ISSN: 1073-7928, DOI: 10.1093/imrn/rnx145
International Mathematics Research Notices 2019-05-28
2016 In-Jee Jeong, Sasha Sodin
A limit theorem for stochastically decaying partitions at the edge
published pages: 1650016, ISSN: 2010-3263, DOI: 10.1142/S2010326316500167
Random Matrices: Theory and Applications 05/04 2019-05-27

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