Harold Widom

Photographer: Peter Webber
Harold Widom

Professor Emeritus
University of California
Santa Cruz


Ph.D. University of Chicago 1955
M.S. University of Chicago 1952
City College of New York, 1951

Office: 133B Kerr Hall

Phone: 831-459-2652

Fax: 831-459-3260

E-mail: widom@math.ucsc.edu

Another Widom on the web is daughter Jennifer.


Research Interests
Honors and Awards
Recent Publications
Full Publication List
Ph.D. Students


Research Interests

Harold Widom's early research was in the areas of integral equations and operator theory, in particular the determination of the spectra of semi-infinite Toeplitz matrices and Wiener-Hopf operators and the asymptotic behavior of the spectra of various classes of operators. The latter was looked at from the point of view of pseudodifferential operators (which generalize both integral and partial differential operators) on manifolds, and some new and unifying spectral asymptotic results were obtained using this approach.

A more recent interest is the theory of random matrices, which has become a very active area of research by mathematicians and physicists. For some questions integral operators play a central role. Widom has, with collaborators, used ideas from operator theory to obtain new results in random matrix theory. One such is the explicit representation in terms of Painlevé transcendents of the limiting distributions of the largest and smallest eigenvalues in many models of random matrices. These same distributions have since been shown to arise in numerous other physical models, in random growth models, and in asymptotic combinatorics.

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Honors and Awards

George Polya Prize of SIAM (shared with Craig A. Tracy), 2002

Guggenheim Foundation Fellowship, 1972-73

Guggenheim Foundation Fellowship, 1967-68

Sloan Foundation Fellowship, 1964-65

NSF Postdoctoral Fellowship, 1959-60

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Ph.D. Students

Bin Shao, 1993. Second Order Asymptotics for the Discrete Analogue of a Class of Pseudodifferential Operators

Bobette Thorsen, 1992. An Asymptotic Expansion for the Trace of Certain Integral Operators

Shuxian Lou, 1992. The Second Order Asymptotics of a Class of Integral Operators with Discontinuous Symbols

Xiang Fu, 1991. Asymptotics of Toeplitz Matrices with Symbols of Bounded Variations

Richard Libby, 1990. Asymptotics of Determinants and Eigenvalue Distributions for Toeplitz Matrices Associated with Certain Discontinuous Symbols

Ray Roccaforte, 1982. Asymptotic Expansions of Traces for Certain Convolution Operators

Estelle Basor, 1975. Asymptotic Formulas for Toeplitz Determinants

Lidia Luquet, 1972. p-Norm Inequalities for Entire Functions

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Last updated, January 29, 2003.