Harold Widom | Academic Influence

Harold Widom's AcademicInfluence.com Rankings

Harold Widom

Mathematics

#708

World Rank

#1295

Historical Rank

#308

USA Rank

Measure Theory

#973

World Rank

#1264

Historical Rank

#363

USA Rank

mathematics Degrees

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Mathematics

Harold Widom's Degrees

PhD Mathematics Princeton University

Why Is Harold Widom Influential?

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According to Wikipedia, Harold Widom was an American mathematician best known for his contributions to operator theory and random matrices. He was appointed to the Department of Mathematics at the University of California, Santa Cruz in 1968 and became professor emeritus in 1994.

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Harold Widom's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Level-spacing distributions and the Airy kernel (1992) (1813)
Introduction to Random Matrices (1992) (1466)
On orthogonal and symplectic matrix ensembles (1995) (915)
Fredholm determinants, differential equations and matrix models (1993) (363)
Level spacing distributions and the Bessel kernel (1993) (342)
Extremal polynomials associated with a system of curves in the complex plane (1969) (323)
Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices (1998) (293)
Asymptotics in ASEP with Step Initial Condition (2008) (265)
Asymptotic behavior of block Toeplitz matrices and determinants. II (1974) (262)
Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models (2000) (212)
Integral Formulas for the Asymmetric Simple Exclusion Process (2007) (211)
Eigenvalue distribution of time and frequency limiting (1980) (202)
Toeplitz Determinants with Singular Generating Functions (1973) (160)
Inversion of Toeplitz matrices II (1959) (145)
Asymptotic behavior of the eigenvalues of certain integral equations (1963) (142)
Distribution Functions for Largest Eigenvalues and Their Applications (2002) (135)
On the distributions of the lengths of the longest monotone subsequences in random words (1999) (131)
A Fredholm Determinant Representation in ASEP (2008) (131)
The Pearcey Process (2004) (122)
The Distribution of the Largest Eigenvalue in the Gaussian Ensembles: β = 1, 2, 4 (1997) (116)
Random Unitary Matrices, Permutations and Painlevé (1998) (105)
Review: I. C. Gohberg and I. A. Fel′dman, Convolution equations and projection methods for their solution (1975) (104)
On the eigenvalues of certain Hermitian operators (1958) (102)
The Strong Szego Limit Theorem for Circular Arcs (1971) (98)
On the Relation Between Orthogonal, Symplectic and Unitary Matrix Ensembles (1998) (96)
On the spectrum of a Toeplitz operator. (1964) (92)
Differential Equations for Dyson Processes (2003) (91)
Communications in Mathematical Physics The Pearcey Process (2006) (89)
Proofs of two conjectures related to the thermodynamic Bethe Ansatz (1995) (83)
Random Words, Toeplitz Determinants and Integrable Systems. II (1999) (82)
Singular integral equations in _ (1960) (80)
Asymptotic behavior of the eigenvalues of certain integral equations. II (1964) (79)
On a Toeplitz determinant identity of Borodin and Okounkov (1999) (77)
Nonintersecting Brownian Excursions (2006) (76)
The Distributions of Random Matrix Theory and their Applications (2009) (71)
H p Sections of Vector Bundles Over Riemann Surfaces (1971) (66)
On a Class of Integral Operators with Discontinuous Symbol (1982) (61)
On ASEP with Step Bernoulli Initial Condition (2009) (61)
The Asymptotics of a Continuous Analogue of Orthogonal Polynomials (1994) (59)
Toeplitz and Wiener-Hopf determinants with piecewise continuous symbols (1983) (57)
Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains (1985) (56)
From Toeplitz Eigenvalues through Green’s Kernels to Higher-order Wirtinger-Sobolev Inequalities (2004) (55)
Matrix kernels for the Gaussian orthogonal and symplectic ensembles (2004) (52)
Extreme eigenvalues of translation kernels (1961) (52)
Fredholm determinants and the mKdV/Sinh-Gordon hierarchies (1995) (49)
Rational approximation and n-dimensional diameter☆ (1972) (48)
Szegö via Jacobi (2006) (44)
Hamiltonian Structure of Equations Appearing in Random Matrices (1993) (44)
On the limit of block Toeplitz determinants (1975) (42)
Extreme eigenvalues of $N$-dimensional convolution operators (1963) (42)
Szegö's limit theorem: The higher-dimensional matrix case☆ (1980) (42)
Universality of the distribution functions of random matrix theory (1999) (40)
Eigenvalue distribution theorems for certain homogeneous spaces (1979) (39)
On exact solutions to the cylindrical Poisson-Boltzmann equation with applications to polyelectrolytes (1997) (39)
On the Singular Values of Toeplitz Matrices (1989) (37)
Determinants of Airy Operators and Applications to Random Matrices (1998) (36)
The circumference of a convex polygon (1961) (36)
A SYSTEM OF DIFFERENTIAL EQUATIONS FOR THE AIRY PROCESS (2003) (36)
Asymptotics of a Class of Solutions to the Cylindrical Toda Equations (1997) (35)
Lectures on Integral Equations (1969) (35)
On Asymptotics for the Airy Process (2003) (34)
Total Current Fluctuations in ASEP (2009) (34)
A Limit Theorem for Shifted Schur Measures (2002) (34)
Toeplitz Operators with Locally Sectorial Symbols (1970) (32)
A growth model in a random environment (2000) (32)
A THEOREM ON TRANSLATION KERNELS IN n DIMENSIONS( (1960) (31)
Asymptotics for the Fredholm determinant of the sine kernel on a union of intervals (1994) (30)
Determinants of Hankel Matrices (2000) (30)
Embedding in algebras of type I (1956) (30)
Stable processes and integral equations (1961) (29)
On convergence of moments for random Young tableaux and a random growth model (2001) (29)
The maximum principle for multiple-valued analytic functions (1971) (29)
Airy Kernel and Painleve II (1999) (27)
On the Asymmetric Simple Exclusion Process with Multiple Species (2011) (24)
On the Limiting Distribution for the Length of the Longest Alternating Sequence in a Random Permutation (2006) (24)
On the Solution of a Painlevé III Equation (2000) (24)
On a class of integral operators on a half-space with discontinuous symbol (1990) (24)
Painlevé Functions in Statistical Physics (2009) (23)
The dynamics of the one-dimensional delta-function Bose gas (2008) (23)
On the ground state energy of the δ-function Bose gas (2016) (22)
The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line (2012) (22)
Model for line tension in three-phase equilibrium (1991) (21)
Erratum to: Integral Formulas for the Asymmetric Simple Exclusion Process (2011) (21)
Eigenvalue Distribution for Nonselfadjoint Toeplitz Matrices (1994) (21)
Two Elementary Derivations of the Pure Fisher-Hartwig Determinant (2003) (20)
Formulas for ASEP with Two-Sided Bernoulli Initial Condition (2010) (18)
Asymptotic inversion of convolution operators (1974) (18)
Some Classes of Solutions to the Toda Lattice Hierarchy (1996) (18)
Small eigenvalues of large Hankel matrices (1966) (18)
Fluctuations in the Composite Regime of a Disordered Growth Model (2001) (17)
On the Limit of Some Toeplitz-Like Determinants (2001) (17)
The Laplace operator with potential on the 2-sphere (1979) (17)
The asymmetric simple exclusion process with an open boundary (2013) (15)
On the ground state energy of the delta-function Fermi gas (2016) (14)
Toeplitz operators on Hp (1966) (14)
An Exercise (?) in Fourier Analysis on the Heisenberg Group (2015) (14)
Formulas for Joint Probabilities for the Asymmetric Simple Exclusion Process (2010) (14)
On the distribution of a second-class particle in the asymmetric simple exclusion process (2009) (13)
Perturbing Fredholm operators to obtain invertible operators (1975) (12)
On an inequality of Osgood, Phillips and Sarnak (1988) (12)
A Continuous Analogue of the Fisher-Hartwig Formula for Piecewise Continuous Symbols (1994) (12)
Wiener-Hopf determinants with Fisher-Hartwig symbols (2002) (12)
Szegö’s Theorem and a Complete Symbolic Calculus for Pseudo-Differential Operators (1979) (11)
On the Limiting Distribution for the Longest Alternating Sequence in a Random Permutation (2005) (11)
Two Remarks on Spectral Approximations for Wiener-Hopf Operators (1994) (11)
Toeplitz operators onHp (1966) (11)
An inequality for rational functions (1970) (10)
Hankel Determinants as Fredholm Determinants (2001) (9)
On the Ground State Energy of the Delta-Function Fermi Gas II: Further Asymptotics (2016) (9)
Formulas and Asymptotics for the Asymmetric Simple Exclusion Process (2011) (9)
Determinants of truncated Wiener-Hopf operators with Hilbert-Schmidt kernels and piecewise continuous symbols (1994) (8)
On the eigenvalues of certain canonical higher-order ordinary differential operators (2005) (8)
SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS FOR A CLASS OF OPERATOR DETERMINANTS (1995) (8)
Equations of Wiener-Hopf type (1958) (7)
Blocks in the Asymmetric Simple Exclusion Process (2017) (7)
Asymptotics of a Class of Operator Determinants with Application to the Cylindrical Toda Equations (2006) (7)
Research in Analysis. (1970) (7)
Lectures on Measure and Integration (1969) (7)
Rapidly increasing kernels (1963) (6)
An Integral Operator Solution to the Matrix Toda Equations (1997) (6)
Random Hermitian Matrices and (Nonrandom) Toeplitz Matrices (1994) (6)
On the Determinant of a Certain Wiener-Hopf + Hankel Operator (2003) (6)
Nonisomorphic approximately finite factors (1957) (5)
Recent advances in operator theory and applications (2005) (5)
Useful Bounds on the Extreme Eigenvalues and Vectors of Matrices for Harper’s Operators (2015) (5)
Approximately finite algebras (1956) (4)
Errata to: “Small eigenvalues of large Hankel matrices” (1968) (4)
Toeplitz Determinants, Random Matrices and Random Permutations (2002) (4)
On the Solution of a Painlev\'e III Equation (1998) (4)
Blocks and gaps in the asymmetric simple exclusion process: Asymptotics (2017) (4)
On a functorial property of power residue symbols (1974) (4)
On Wiener-Hopf Determinants (1989) (4)
On the diagonal susceptibility of the 2D Ising model (2013) (4)
Asymptotics of a Class of Operator Determinants (2005) (3)
On ASEP with Periodic Step Bernoulli Initial Condition (2010) (3)
On the Distributions of the Lengths of the Longest Increasing and Decreasing Subsequences in Random Words (1999) (3)
On asymmetric simple exclusion process with periodic step Bernoulli initial condition (2011) (2)
Symbols and Asymptotic Expansions (1992) (2)
On the Inverse and Determinant of a Truncated Wiener-Hopf Operator (2006) (2)
Asymptotics of a class of Fredholm determinants (1998) (2)
A two-sided absorption problem (1961) (1)
Pseudo-Differential Operators (1987) (1)
Schatten Class Integral Operators Occurring in Markov-type Inequalities (2016) (1)
On the Inverse and Determinant of Certain Truncated Wiener-Hopf Operators (2006) (1)
Two extremal problems. (1960) (1)
On the Singularities in the Susceptibility Expansion for the Two-Dimensional Ising Model (2014) (1)
Derivation of the series (1985) (0)
A ug 2 00 3 On Asymptotics for the Airy Process (0)
The Thermodynamic Bethe Ansatz and a Connection with Painlevé Equations (1997) (0)
Natural Boundary for a Sum Involving Toeplitz Determinants (2015) (0)
Domain Walls in the Heisenberg-Ising Spin-1/2 Chain (2022) (0)
Asymptotic expansions and stationary phase for operators with discontinuous symbol (1994) (0)
STABLE PROCESSES AND INTEGRAL (2010) (0)
Proof of the Szegö expansion in the self-adjoint case (1985) (0)
The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line (2013) (0)
Spectral asymptotics of hypersurfaces (1978) (0)
Proof of the heat expansion (1985) (0)
The Heat Expansion for Systems of Integral Equations (1988) (0)
Blocks in the Asymmetric Simple Exclusion Process: Asymptotics (2017) (0)
An Elementary Derivation of the Fisher-Hartwig Determinant (2003) (0)
On a Distribution Function Arising in Computational Biology (2000) (0)
determinants with singular generating functions (2022) (0)
Given finite or infinite intervals I and J we con sider the integral operator on L2(I) with kernel (1982) (0)
Asymptotics for an Individual Particle in ASEP (2008) (0)
In Memoriam: Freeman Dyson (1923–2020) (2021) (0)
J un 2 00 4 June 1 , 2004 Differential Equations for Dyson Processes (0)
A pr 2 00 6 Szegö via (0)
On the Singularities in the Susceptibility Expansion for the Two-Dimensional Ising Model (2014) (0)
Shorter Note: An Inequality for Rational Functions (1970) (0)
FA ] 1 A pr 2 00 6 Szegö via Jacobi (2018) (0)
Random Matrix Models and Their Applications January 19 – 23 , 1999 Airy Kernel and Painlevé II (0)
The Szegö and heat expansions (1985) (0)
Ju l 2 00 9 July 29 , 2009 On ASEP with Step Bernoulli Initial Condition (2009) (0)
On Some Extremal Quantities Associated with Unbounded Sets in the Plane (1969) (0)
Integral Operators in Random Matrix Theory (2011) (0)
On the Asymmetric Simple Exclusion Process with Multiple Species (2012) (0)
Proof of the szegö expansion in the nonself-adjoint case (1985) (0)
On the Diagonal Susceptibility of the 2 D Ising Model (2021) (0)
Communications in Mathematical Physics Asymptotics in ASEP with Step Initial Condition (2008) (0)
Inversion of an integral transform (1958) (0)
2 3 A pr 2 00 4 April 23 , 2004 Differential Equations for Dyson Processes (0)
A pr 1 99 8 On Orthogonal and Symplectic Matrix Ensembles Associated with a Class of Weight Functions (1998) (0)
A Note on Convergence of Moments for Random Young Tableaux (2001) (0)
STOCHASTIC MODELING IN THE SCIENCES: STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND RANDOM MEDIA (2005) (0)
More about Pseudodifferential Operators on Bounded Domains (1986) (0)
f(k)(σ; τi) in the hermitian case (1985) (0)
PR ] 4 S ep 2 00 3 Differential Equations for Dyson Processes (0)
A Growth Model in a Random Environment a Growth Model in a Random Environment (2000) (0)
Elias M. Stein (1931–2018) (2021) (0)
Pseudo-differential operators : proceedings of a conference held in Oberwolfach, February 2-8, 1986 (1987) (0)
A Growth Model in a Random Environment 1 (2005) (0)

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