Institute for Mathematical Sciences Programs & Activities
Random Matrix Theory and its Applications II
(18 Jun - 15 Aug 2012)
- Ying-Chang Liang (Institute for Infocomm Research)
- Zhidong Bai (Northeast Normal University and National University of Singapore)
- Yang Chen (Imperial College London)
- Alan Edelman (Massachusetts Institute of Technology)
- Guangming Pan (Nanyang Technological University)
- Wang Zhou (National University of Singapore)
Random matrix theory (RMT) originated from multi-variate statistics and nuclear physics, and flourished into a branch of mathematical physics under the strong impetus of Dyson, Gaudin, Mehta, Wigner and others in the 1960's and 1970's. Further stimulus came in the early 1990's because of the resurgent in low dimensional string theory mainly through effort of Brezin, Kazakov, Gross, Migdal and others.
The next high water mark arrived with the remarkable discovery by Tracy and Widom probability laws that govern the distribution function of extreme eigenvalues of certain large Hermitian random matrices, what is particularly striking is that the distributions are solutions of a class non-linear differential equations, known as the Painleve equations first discovered around 1905 by Painleve and his collaborators. An explosion of activities have since followed, initially in theoretical areas but has now broken into applied mathematics for example high dimensional inferences in principle component analysis (Johnstone) and wireless communications in electrical engineering through the pioneering work of Telatar and Foschini. And most recently random matrix theory has permeated into the field of interacting particle systems and exactly solvable models in non-equilibrium transport. These areas share a common theme: Regularity emerges from complex and random systems when the number of structure-less constituents (eigenvalues) becomes large.
In addition to the third edition of Mehta's classic "Random Matrices", one finds the recent contributions to the field of Bai and Silverstrein's "Spectral analysis of large dimensional random matrices", Blower's "Random matrices: High dimensional phenomena" and "An introduction to random matrices" of Anderson, Guionnet and Zeitouni, all testify the tremendous relevance and vitality of the field.
Besides its long history and recent tremendous advances, RMT has emerged as an extremely powerful tool for a variety of applications, especially in statistical signal processing, wireless communications, finance statistics and bioinformatics. For example, RMT has become the key ingredient for designing and analyzing detection and estimation techniques in array signal processing as well wireless communications. The large-dimensional RMT results have been used to design multiantenna wireless systems and multiuser detection schemes and to analyze the information-theoretic limits of multidimensional wireless channels. The two-month program will provide the mathematicians and engineers a unique platform to discuss interesting fundamental problems, results and explore possible solutions related to RMT and its applications in wireless communications and statistics.
- Informal seminars, ad hoc talks and discussions: 18 Jun - 6 Jul 2012
- Tutorial 1: 10 - 16 Jul 2012
- Workshop 1 - RMT Applications in Wireless Communications: 18 - 25 Jul 2012
- Tutorial 2: 30 Jul - 2 Aug 2012
- Workshop 2 - RMT Applications in Statistics: 7 - 15 Aug 2012
* Our office will be closed on the Thursday, 9 Aug 2012 - National Day, being Singapore public holiday.
Students and researchers who are interested in attending these activities are requested to complete the online registration form.
The following do not need to register:
- Those invited to participate.
For general enquiries, please email us at ims(AT)nus.edu.sg.
For enquiries on scientific aspects of the program, please email Ying-Chang Liang at ycliang(AT)i2r.a-star.edu.sg.