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Harold Widom Professor Emeritus University of California Santa Cruz
Ph.D. University of Chicago 1955 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.
Guggenheim Foundation Fellowship, 1972-73
Guggenheim Foundation Fellowship, 1967-68
Sloan Foundation Fellowship, 1964-65
NSF Postdoctoral Fellowship, 1959-60
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
