جنبه‌های مدرن نظریه ماتریس تصادفی: دورهٔ کوتاه AMS، ماتریس‌های تصادفی، ۶-۷ ژانویه ۲۰۱۳، سن دیگو، کالیفرنیا

The theory of random matrices is an amazingly rich topic in mathematics. Random matrices play a fundamental role in various areas such as statistics, mathematical physics, combinatorics, theoretical computer science, number theory and numerical analysis. This volume is based on lectures delivered at the 2013 AMS Short Course on Random Matrices, held January 6–7, 2013 in San Diego, California. Included are surveys by leading researchers in the field, written in introductory style, aiming to provide the reader a quick and intuitive overview of this fascinating and rapidly developing topic. These surveys contain many major recent developments, such as progress on universality conjectures, connections between random matrices and free probability, numerical algebra, combinatorics and high-dimensional geometry, together with several novel methods and a variety of open questions. Content: Lecture notes on the circular law by C. Bordenave and D. Chafai Free probability and random matrices by A. Guionnet Random matrix theory, numerical computation and applications by A. Edelman, B. D. Sutton, and Y. Wang Recent developments in non-asymptotic theory of random matrices by M. Rudelson Random matrices: The universality phenomenon for Wigner ensembles by T. Tao and V. Vu Index