Craig Tracy

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Craig Arnold Tracy (born September 9, 1945 in London ) is an American theoretical physicist and mathematician.

Craig Tracy

Tracy was born the son of a US soldier stationed in England and a British woman and grew up in Missouri . He studied physics at the University of Missouri (Bachelor 1967) and Columbia University and received his PhD in physics from the State University of New York at Stony Brook (SUNY) in 1973 with Barry McCoy . As a Post Doc he was at the University of Rochester , SUNY and Los Alamos National Laboratory . From 1978 he was an assistant professor of mathematics at Dartmouth College , where he became an associate professor in 1983. Since 1984 he has been Professor of Mathematics at the University of California, Davis . From 1994 to 1998 he was head of the mathematics faculty there, and has been a Distinguished Professor since 2003. In 1992 and 2001/02 he was director of the Institute for Theoretical Dynamics in Davis. Among other things, he was visiting professor at the RIMS in Kyoto .

As a student of McCoy, he initially dealt with aspects of the Ising model of statistical mechanics, in particular exact formulas for the correlation functions in the two-dimensional scaling limit case (with McCoy, Tai Tsun Wu ), but also with other grid models.

He became known for his research with Harold Widom on random matrices and their applications. Here they generalized a formula for the density of states of the eigenvalues ​​of random matrices, which Michio Jimbō , Mikio Satō , Tetsuji Miwa and Mori first stated in 1980 for the GUE (Gaussian Unitary Ensemble). The formula examined by Tracy and Widom gives the density of states as the Fredholm determinant of an integral operator, whereby the two functions occurring in the core of the integral operator satisfy coupled linear differential equations. The existing differential equations of the Painleve type also appeared in the work of Tracy, McCoy, Wu and Barouch on correlation functions in the Ising model (1976).

Harold Widom (left) with Craig Tracy (right)

Tracy and Widom also introduced new distribution functions in their work (Tracy-Widom distributions), with applications in stochastics and combinatorics (such as the longest increasing subsequence problem by Stanislaw Ulam , pavements , random walks ).

1967/68 he was a Woodrow Wilson Fellow. In 2002 he received the George Pólya Prize of the Society for Industrial and Applied Mathematics (SIAM) with Widom and the Norbert Wiener Prize in 2007 . He has been a Fellow of the American Academy of Arts and Sciences since 2006 . He is a fellow of the American Mathematical Society .

Fonts

  • with Widom: Fredholm Determinants, Differential Equations and Matrix Models, Comm. Math. Phys., Vol. 163, 1994, pp. 33-72, Arxiv
  • with Widom: Level-Spacing Distributions and the Airy Kernel, Comm. Math. Phys. Vol. 159, 1974, pp. 151-174, Arxiv
  • with Widom: Introduction to Random Matrices, Springer, Lecture Notes in Physics 424, 1993, pp. 103-130, Arxiv

Web links

References

  1. Life data according to American Men and Women of Science , Thomson Gale 2004
  2. At that time, they did not primarily investigate random matrices, but models of statistical mechanics and quantum field theory
  3. for example exponential function, Airy and Bessel functions , Hermite polynomials
  4. Craig Tracy, Harold Widom, Fredholm determinants, differential equations and matrix models, Comm. Math. Phys., Vol. 163, 1994, pp. 33-72
  5. Tracy, Widom, Level spacing distributions and the Airy Kernel, Comm. Math. Phys., Vol. 159, 1994, pp. 151-174
  6. ^ TT Wu, BM McCoy, C..A. Tracy, E. Barouch, Spin-spin correlation functions for the two dimensional Ising model: exact theory in the scaling region, Physical Review B, Volume 13, 1976, 316-374