數學系智慧大樹
◎講者：王俊超教授(Jiun-Chau Wang)
◎現職：University of Saskatchewan, Canada
◎時間：99年12月21日（星期二），下午2點30分至3點30分
◎地點：S433
◎講題：Free Convolution and Random Matrices
◎摘要

The past decade has seen many advances in wireless communication theory and their implementation in wireless systems. Matrices with randomly sampled entries, the so-called random matrices, come naturally into the play due to the varying characteristics of the wireless network systems.
Researchers found that the performance measurement for many multiuser wireless systems is relative to the limiting behavior of the corresponding random matrix models when the size of the matrices go without bound.
Free probability provides a right framework for studying such a behavior. It was invented by Dan Voiculescu in 1983 in order to understand the structure of certain von Neumann algebras.
His discovery in 1991 that large random matrices satisfy asymptotically the freeness condition changed the theory dramatically and brought new concepts and tools into the random matrix theory.
Examples include free convolution and R- and S-transforms. Moreover, in recent years, engineers started to apply free probability tools to solve problems in wireless communications, and this has made free probability an interesting and important field for applied scientists.
This talk will be a survey on the theory of free convolution and some of its applications to random matrices, with an emphasis on the complex and harmonic analysis side.

◎會後與學生分享座談：下午3點40分至5點30分。

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