Harold Widom

Photographer: Linda Larkin
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: McHenry 4176

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
Selected 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 study of Toeplitz 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 on manifolds, and some new and unifying spectral asymptotic results were obtained using this approach.

A later interest was the theory of random matrices, an 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.

A current interest, in the interface between statistical mechanics and probability, is interacting particle systems. In collaboration with Craig A. Tracy both exact and asymptotic formulas were obtained for the asymmetric simple exclusion process, a stochastic model for transport phenomena. These results have had application to questions of universality in mathematical physics. Back to the top

Honors and Awards

University of California Edward A. Dickson Emeriti Professorship 2007/08

Fellow of The American Academy of Arts and Sciences 2007

Norbert Wiener Prize of AMS and SIAM (shared with C. A. Tracy), 2007

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 May 18, 2013.