Harold Widom (September 23, 1932 – January 20, 2021) was an American mathematician best known for his contributions to

operator theory In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear oper ...

and

random matrices In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathemat ...

. He was appointed to the Department of Mathematics at the

University of California, Santa Cruz The University of California, Santa Cruz (UC Santa Cruz or UCSC) is a public land-grant research university in Santa Cruz, California. It is one of the ten campuses in the University of California system. Located on Monterey Bay, on the edge ...

in 1968 and became

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

in 1994.

Education and research

Widom was born in

Newark, New Jersey Newark ( , ) is the List of municipalities in New Jersey, most populous City (New Jersey), city in the U.S. state of New Jersey and the county seat, seat of Essex County, New Jersey, Essex County and the second largest city within the New Yo ...

. He studied at

Stuyvesant High School Stuyvesant High School (pronounced ), commonly referred to among its students as Stuy (pronounced ), is a State school, public university-preparatory school, college-preparatory, Specialized high schools in New York City, specialized high school ...

, graduating in 1949, and was a member of the school's math team along with his brother

Benjamin Widom Benjamin Widom (born 13 October 1927) is the Goldwin Smith Professor of Chemistry at Cornell University. His research interests include physical chemistry and statistical mechanics. In 1998, Widom was awarded the Boltzmann Medal "for his illum ...

(1944, 1948). Widom attended

City College of New York The City College of the City University of New York (also known as the City College of New York, or simply City College or CCNY) is a public university within the City University of New York (CUNY) system in New York City. Founded in 1847, Cit ...

until 1951, during which he was one of the winners of the

William Lowell Putnam Mathematical Competition The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regard ...

(1951). At the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

he obtained an M.S. (1952) and

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

, the latter on a thesis ''Embedding of AW*-algebras'' advised by

Irving Kaplansky Irving Kaplansky (March 22, 1917 – June 25, 2006) was a mathematician, college professor, author, and amateur musician.O'Connor, John J.; Robertson, Edmund F., "Irving Kaplansky", MacTutor History of Mathematics archive, University of St And ...

(1955). He taught mathematics at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to ...

(1955–68) where he started his work on Toeplitz and Wiener-Hopf operators, partly inspired by

Mark Kac Mark Kac ( ; Polish: ''Marek Kac''; August 3, 1914 – October 26, 1984) was a Polish American mathematician. His main interest was probability theory. His question, " Can one hear the shape of a drum?" set off research into spectral theory, the ...

. Widom was appointed in the Department of Mathematics at the

, and became

in 1994. His research areas were in

integral equations In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ...

and

, in particular the determination of the spectra of a semi-infinite

Toeplitz matrix In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix: :\qquad\begin a & b ...

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 In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory, e.g. in ...

(which generalize both integral and partial differential operators) on manifolds. More recently, his mathematical contributions with his long-term collaborator Craig Tracy have been recognized through the award of several prizes for their joint work on

Tracy–Widom distribution The Tracy–Widom distribution is a probability distribution from random matrix theory introduced by . It is the distribution of the normalized largest eigenvalue of a random Hermitian matrix. The distribution is defined as a Fredholm determinant ...

functions for

. They used integral operators to obtain explicit representations, in terms of

Painlevé transcendents In mathematics, Painlevé transcendents are solutions to certain nonlinear second-order ordinary differential equations in the complex plane with the Painlevé property (the only movable singularities are poles), but which are not generally solvabl ...

, of the limiting distributions of the largest and smallest eigenvalues in many models of random matrices (see

Fredholm determinant In mathematics, the Fredholm determinant is a complex-valued function which generalizes the determinant of a finite dimensional linear operator. It is defined for bounded operators on a Hilbert space which differ from the identity operator by a tr ...

s). These same distributions have since been shown to arise in numerous other physical models, in random growth models, and in

asymptotic combinatorics In combinatorics, the symbolic method is a technique for counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions. The method is mostly associated with Philippe Flajolet and ...

. He has been the author of two books and more than 120 journal articles, and was an associate editor of ''Asymptotic Analysis'', ''Journal of Integral Equations and Applications and Mathematical Physics'', ''Analysis'', and ''Geometry''. He was an honorary editor of

Integral Equations and Operator Theory ''Integral Equations and Operator Theory'' is a journal dedicated to operator theory and its applications to engineering and other mathematical sciences. As some approaches to the study of integral equations (theoretically and numerically) constit ...

. Widom died from complications of

COVID-19 Coronavirus disease 2019 (COVID-19) is a contagious disease caused by a virus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first known case was identified in Wuhan, China, in December 2019. The disease quickl ...

at his home in

Santa Cruz, California Santa Cruz ( Spanish for "Holy Cross") is the county seat and largest city of Santa Cruz County, in Northern California. As of the 2020 census, the city population was 62,956. Situated on the northern edge of Monterey Bay, Santa Cruz is a pop ...

, on January 20, 2021, at age 88.

Awards

*Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

, 2012List of Fellows of the American Mathematical Society
retrieved 2013-09-01. * Norbert Wiener Prize in Applied Mathematics 2006, shared with Craig Tracy2007 Wiener Prize
/ref> *

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, ...

elected, 2006 *

George Pólya Prize The Society for Industrial and Applied Mathematics (SIAM) has three prizes named after George Pólya: the George Pólya Prize for Mathematical Exposition, established in 2013; the George Pólya Prize in Applied Combinatorics, established in 1969 ...

2002, shared with Craig Tracy, for their work on

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

1967 and 1972 *

Sloan Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

1964–65 *

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National ...

Postdoctoral Fellowship, 1959–60

Notes

Bibliography

*. (The proceedings of this 60th birthday conference contain a short biography by Estelle L. Basor and Edward M. Landesman.)

External links

* * * {{DEFAULTSORT:Widom, Harold 1932 births 2021 deaths Deaths from the COVID-19 pandemic in California 20th-century American mathematicians 21st-century American mathematicians Scientists from New York City Stuyvesant High School alumni City College of New York alumni University of Chicago alumni Cornell University faculty University of California, Santa Cruz faculty Fellows of the American Mathematical Society People from Newark, New Jersey Mathematicians from New Jersey Mathematicians from New York (state) Putnam Fellows