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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

Workshop on

Random Matrices and Related Topics

Monday 13 - Friday 17 January, 2003
Sandbjerg Estate, Denmark

Random matrices have been of great importance in statistics since the work of J. Wishart (1928) and P.L. Hsu (1939).

In the 1950's E.P. Wigner used random matrices in an attempt to model the energy levels at nuclear reactions in quantum physics. He discovered, in particular, that the spectral distribution of a selfadjoint (Gaussian) n-by-n random matrix is, asymptotically (as n tends to infinity), the semi-circle distribution. Since then, random matrices have played a significant role in various fields of mathematics and physics.

In the 1980's, D.V. Voiculescu introduced the notion of free independence, and he proved that independent selfadjoint (Gaussian) n-by-n random matrices are asymptotically (as n tends to infinity) freely independent. This discovery has lead to a number of important applications of random matrices in operator algebra theory.

Another breakthrough in the theory of random matrices came in the 1990's, when C. Tracy and H. Widom found, for any fixed number k, the asymptotic (as n tends to infinity) joint distribution of the k largest eigenvalues of a selfadjoint Gaussian n-by-n random matrix (in the real, complex and quaternionic cases). These results have had great impact on the theory of longest increasing subsequences for random permutations.

Random matrices are also of great importance in analytical number theory, in particular for problems concerning the distribution of zeroes for the Riemann zeta-function and the Dirichlet L-series. This fact is well-documented in the monograph Random matrices, Frobenius eigenvalues, and monodromy by P. Sarnak and N.M. Katz.

Last, but not least, random matrices play a crucial role in many applied areas as well. We mention, in particular, areas like signal processing and neural networks which have been studied extensively by U. Grenander, J.W. Silverstein and others by virtue of random matrices.

The aim of the workshop is to bring together scientists working with the various aspects of random matrix theory, with the purpose of presenting the state of the art in each of these fields and illuminating the interrelations.

The workshop will be held at Sandbjerg Manor, a conference centre owned by the University of Aarhus, situated in the southern part of Jutland, Denmark.


Ole E. Barndorff-Nielsen, University of Aarhus
Uffe Haagerup, University of Southern Denmark Odense
Steen Thorbjørnsen, University of Southern Denmark Odense


Monday, January 13

09:00-10:00: Dan Voiculescu: Free probability topics
10:00-10:25: Coffee/tea
10:25-11:10: Dimitri Shlyaktenko: On Voiculescu's non-microstates free entropy
11:15-12:00: Alexandru Nica: Annular non-crossing permutations, and second-order asymptotics for random matrices
12:15-13.15: Lunch
15:00-15:30: Coffee/tea
15:30-16:15: Fumio Hiai: Free pressure and random matrix perturbations
16:20-17:05: Denes Petz: TBA
17:15-18:00: Marek Bozejko: Generalized Brownian motions associated with Thoma characters of infinite permutation groups
18:00: Dinner
20:30: Get-together

Tuesday, January 14

09:00-10:00: Hari Bercovici: Eigenvalue inequalities in a von Neumann algebra
10:00-10:25: Coffee/tea
10:25-11:10: Jack Silverstein: CLT for linear spectral statistics of large dimensional sample covariance matrices
11:15-12:00: Zhidong Bai: On the convergence of the spectral empirical process of Wigner matrices
12:15-13.15: Lunch
15:00-15:30: Coffee/tea
15:30-16:15: Gilles Pisier: Applications of matrix models to the study of operator spaces
16:20-17:05: Gérard Letac: The explicit computation of the moments of the Wishart distribution
17:15-18:00: Mireille Capitaine and Muriel Cassalis: Asymptotic freeness by generalized moments. Application to Wishart and Beta matrices
18:00: Dinner

Wednesday, January 15

09:00-10:00: Alexander Gamburd: Expander graphs, random matrices, and quantum chaos
10:00-10:30: Coffee/tea
10:30-11:15: Nina Snaith: Random matrix theory and the Riemann zeta function
11:20-11:50: Francesco Mezzadri: Random matrix theory and the zeros of zeta(s)
12:15-13.15: Lunch
13:30-17.30: Excursion
18:00: Dinner

Thursday, January 16

09:00-10:00: Alexander Soshnikov: On Janossy densities in determinantal and pfaffian ensembles
10:00-10:25: Coffee/tea
10:25-11:10: Boris Khoruzhenko: Random circulant Jacobi matrices
11:15-12:00: Romuald Janik: Explicit factorization of Seiberg-Witten curves with matter from random matrix models
12:15-13.15: Lunch
15:00-15:30: Coffee/tea
15:30-16:15: Jan Ambjørn: A matrix model description of 3d quantum gravity.
16:20-16:50: Franz Lehner: Noncommutative cummulants and characterizations of generalized Gaussian random variables
17:10-17:40: Arno Kuijlaars: Density of states in a 2-matrix model
17:45-18:15: Madalin Guta: Sieve maximum likelihood estimation of the density matrix through quantum demography
19:00: Conference dinner

Friday, January 17

09:00-10:00: Anatoly Vershik: Fock factorizations and the processes with independent values
10:00-10:25: Coffee
10:25-11:10: Stanislaw Szarek: TBA
11:15-12:00: Benoit Collins: Itzykson-Zuber type integrals and free probability
12:15-13.15: Lunch
13.15-14.00: Piotr Sniady: Non-hermitian operators, random matrices and Brown spectral measure
14.05-14.50: Ken Dykema: Invariant subspaces for operators modeled by certain upper triangular random matrices


No financial support is available. Participants are expected to have their expenses covered by their home institutions.


The registration fee is DKK 500, payable upon arrival at Sandbjerg in cash in Danish currency.

List of Participants

Travel information: How to reach Sandbjerg Estate

Sandbjerg is located in South Jutland, close to the German border.
Address: Sandbjerg Manor, Sandbjergvej 102, DK-6400 Sønderborg

By airplane: Flights from Copenhagen Airport to Sønderborg: 8:00-8:40, 11:00-11.40, 14:55-15:35 (Monday-Friday); 17:15-17:55 (Monday-Friday and Sunday); 20:15-20:55 (Wednesday-Sunday); 18:15-18:55 (Monday-Friday and Sunday).

Flights from Sønderborg to Copenhagen Airport: 7:00-7:40 (Monday-Friday); 7:45-8:25 (Saturday); 9:05-9:45 (Monday-Friday); 12:30-13:10 (Monday-Friday); 15:55-16:35 (Monday-Friday and Sunday); 18:15-18:55 (Monday-Friday and Sunday).

Distance between the airport and Sandbjerg Estate approx.12 km.

By train: Direct train from the airport and from the central railway station of Copenhagen to Sønderborg: Every second hour from 5:30 in the morning to 21:30 in the evening. The travel time is approx. 3 hours and 45 minutes.

Direct train from Sønderborg to the central railway station of Copenhagen: Every second hour from 6:00 in the morning to 20:00 in the evening. The travel time is approx. 3 hours and 45 minutes.

Distance between the railway station and Sandbjerg Estate approx. 7 km.

By car:
From the E45 southbound:
Take exit 71 (Kruså) towards Sønderborg (road no. 41). In Vester Sottrup, 7.6 km before Sønderborg, a sign on the left reads: Sandbjerg 3 km.

From the E45 northbound:
Take exit 75 (Kruså) towards Sønderborg (road no. 8). Driva via Kruså, Rinkenæs and Egernsund to Broager. From here, turn north towards Nybøl and Vester Sottrup where there is a sign which reads: Sandbjerg 3 km.

See the information map.


More Information

Please make further inquiries to MaPhySto (maphysto@maphysto.dk) or to the organizers Ole E. Barndorff-Nielsen (oebn@imf.au.dk), Uffe Haagerup (haagerup@imada.sdu.dk), and Steen Thorbjørnsen (steenth@imada.sdu.dk).

(This announcement is also available in [ postscript-format | pdf-format ])

This document, http://www.maphysto.dk/oldpages/events/RandMat2003/index.html, was last modified January 19, 2004. Questions or comments to the contents of this document should be directed to maphysto@maphysto.dk.