Patterns in Eigenvalues: the 70th Josiah Willard Gibbs Lecture

نویسنده

  • PERSI DIACONIS
چکیده

Typical large unitary matrices show remarkable patterns in their eigenvalue distribution. These same patterns appear in telephone encryption, the zeros of Riemann’s zeta function, a variety of physics problems, and in the study of Toeplitz operators. This paper surveys these applications and what is currently known about the patterns.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Ramifications, Old and New, of the Eigenvalue Problem

Since this is a lecture dedicated to the memory of Josiah Willard Gibbs let me start with that purely mathematical discovery which Gibbs contributed to the theory of Fourier series. Fourier series have to do with the eigenvalues and eigenfunctions of the oldest, simplest, and most important of all spectrum problems, that of the vibrating string. In preparing this lecture, the speaker has assume...

متن کامل

Computer Modeling of Scientific and Mathematical Discovery Processes

Just forty years ago, in Chicago, John von Neumann delivered the eighteenth Josiah Willard Gibbs Lecture. His topic was the ergodic theorem and statistical mechanics. Within a month of that occasion, he and his colleague, Oscar Morgenstern, published their seminal work, The theory of games and economic behavior, applying discrete mathematics to problems of bargaining and competition in economic...

متن کامل

Philosophia Mathematica Advance Access published January 9 , 2006

This is a critical analysis of the first part of Gödel’s 1951 Gibbs lecture on certain philosophical consequences of the incompleteness theorems. Gödel’s discussion is framed in terms of a distinction between objective mathematics and subjective mathematics, according to which the former consists of the truths of mathematics in an absolute sense, and the latter consists of all humanly demonstra...

متن کامل

Mathematics and the Future of Science

It is indeed a great honor to be asked to deliver the Gibbs Lecture this year, and one which I have accepted in a humble spirit. The work of Josiah Willard Gibbs comprised a series of achievements in applied mathematics of such beauty and perfection that the most fitting tribute which could be offered to him here would be a scientific paper written in a spirit of emulation. Such a tribute lies ...

متن کامل

The Annual Meeting in Rochester

The sixty-third Annual Meeting of the American Mathematical Society was held at the University of Rochester on Thursday through Saturday, December 27-29, 1956, in conjunction with meetings of the Mathematical Association of America on Saturday, December 29 and the Association for Symbolic Logic on Thursday, December 27. The registration was 615 including 508 members of the Society. The thirtiet...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003