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Percy Deift

Silver Professor; Professor of Mathematics

1973 …2019
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Research Output 1973 2019

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Article
2019

Universality in numerical computation with random data: Case studies and analytical results

Deift, P. & Trogdon, T., Oct 1 2019, In : Journal of Mathematical Physics. 60, 10, 103306.

Research output: Contribution to journalArticle

Open Access
readers
Numerical Computation
Universality
2018
Orthogonal Polynomials
Logarithmic
Steepest Descent Method
Riemann-Hilbert Problem
Coefficient

The sine process under the influence of a varying potential

Bothner, T., Deift, P., Its, A. & Krasovsky, I., Sep 1 2018, In : Journal of Mathematical Physics. 59, 9, 091414.

Research output: Contribution to journalArticle

sin(x+y)
Fredholm Determinant
determinants
Ensemble
Scaling

Universality for the Toda Algorithm to Compute the Largest Eigenvalue of a Random Matrix

Deift, P. & Trogdon, T., Mar 1 2018, In : Communications on Pure and Applied Mathematics. 71, 3, p. 505-536 32 p.

Research output: Contribution to journalArticle

Largest Eigenvalue
Random Matrices
Universality
Eigenvalues and Eigenvectors
Hermitian matrix
2017
Random Matrix Theory
Integrable Systems
Open Problems
Random process
Random Matrices

Universality for eigenvalue algorithms on sample covariance matrices

Deift, P. & Trogdon, T., Jan 1 2017, In : SIAM Journal on Numerical Analysis. 55, 6, p. 2835-2862 28 p.

Research output: Contribution to journalArticle

Sample Covariance Matrix
Covariance matrix
Universality
Eigenvalue
Eigenvalues and eigenfunctions
2016

On the condition number of the critically-scaled laguerre unitary ensemble

Deift, P., Trogdon, T. & Menon, G., Aug 1 2016, In : Discrete and Continuous Dynamical Systems. 36, 8, p. 4287-4347 61 p.

Research output: Contribution to journalArticle

Condition number
Ensemble
Scaling
Covariance matrix
Tracy-Widom Distribution
2015

On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential I

Bothner, T., Deift, P., Its, A. & Krasovsky, I., Aug 1 2015, In : Communications in Mathematical Physics. 337, 3, p. 1397-1463 67 p.

Research output: Contribution to journalArticle

Scaling Limit
Pi
determinants
Determinant
Asymptotic Behavior
2014

Universality in numerical computations with random data

Deift, P., Menon, G., Olver, S. & Trogdon, T., Oct 21 2014, In : Proceedings of the National Academy of Sciences of the United States of America. 111, 42, p. 14973-14978 6 p.

Research output: Contribution to journalArticle

Numerical Computation
Universality
Sample variance
Numerical Algorithms
Stochastic Algorithms
2013

Toeplitz matrices and toeplitz determinants under the impetus of the ising model: Some history and some recent results

Deift, P., Its, A. & Krasovsky, I., Sep 2013, In : Communications on Pure and Applied Mathematics. 66, 9, p. 1360-1438 79 p.

Research output: Contribution to journalArticle

Toeplitz Determinant
Impetus
Ising model
Toeplitz matrix
Ising Model
2012

Eigenvalues of Toeplitz matrices in the bulk of the spectrum

Deift, P., Its, A. & Krasovsky, I., 2012, In : Bulletin of the Institute of Mathematics Academia Sinica. 7, 4, p. 437-461

Research output: Contribution to journalArticle

2011

An optimal family of exponentially accurate one-bit Sigma-Delta quantization schemes

Deift, P., Krahmer, F. & Gunturk, C. S., Jul 2011, In : Communications on Pure and Applied Mathematics. 64, 7, p. 883-919 37 p.

Research output: Contribution to journalArticle

Delta sigma modulation
Oversampling
Quantization
Decay Rate
Modulation

Asymptotics for a determinant with a confluent hypergeometric kernel

Deift, P., Krasovsky, I. & Vasilevska, J., 2011, In : International Mathematics Research Notices. 2011, 9, p. 2117-2160 44 p.

Research output: Contribution to journalArticle

Determinant
kernel
Fredholm Determinant
Random Matrix Theory
Friedrich Wilhelm Bessel

Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities

Deift, P., Its, A. & Krasovsky, I., Sep 2011, In : Annals of Mathematics. 174, 2, p. 1243-1299 57 p.

Research output: Contribution to journalArticle

Toeplitz Determinant
Hankel Determinant
Hankel
Otto Toeplitz
Singularity

Long-time asymptotics for solutions of the NLS equation with a delta potential and even initial data

Deift, P. & Park, J., 2011, In : International Mathematics Research Notices. 2011, 24, p. 5505-5624 120 p.

Research output: Contribution to journalArticle

Long-time Asymptotics
Nonlinear Equations
Half line
Steepest Descent Method
Robin Boundary Conditions
Long-time Asymptotics
nonlinear equations
Nonlinear Equations
Half line
steepest descent method
2008

Asymptotics of the Airy-Kernel determinant

Deift, P., Its, A. & Krasovsky, I., Mar 2008, In : Communications in Mathematical Physics. 278, 3, p. 643-678 36 p.

Research output: Contribution to journalArticle

Random Matrix Theory
matrix theory
determinants
Hilbert
Determinant
2007

Improved gap estimates for simulating Quantum circuits by adiabatic evolution

Deift, P., Ruskai, M. B. & Spitzer, W., Apr 2007, In : Quantum Information Processing. 6, 2, p. 121-125 5 p.

Research output: Contribution to journalArticle

Quantum Circuits
Networks (circuits)
estimates
Estimate

On the proof of Universality for orthogonal and symplectic ensembles in random matrix theory

Costin, O., Deift, P. & Gioev, D., Oct 2007, In : Journal of Statistical Physics. 129, 5-6, p. 937-948 12 p.

Research output: Contribution to journalArticle

Random Matrix Theory
matrix theory
Universality
Ensemble
Random Matrices

The Widom-Dyson constant for the gap probability in random matrix theory

Deift, P., Its, A., Krasovsky, I. & Zhou, X., May 1 2007, In : Journal of Computational and Applied Mathematics. 202, 1 SPECIAL ISSUE, p. 26-47 22 p.

Research output: Contribution to journalArticle

Random Matrix Theory
sin(x+y)
Trace Class Operators
Constant term
Scaling Limit
Random Matrices
Universality
Ensemble
Polynomials
Scaling Limit

Universality for orthogonal and symplectic Laguerre-type ensembles

Deift, P., Gioev, D., Kriecherbauer, T. & Vanlessen, M., Oct 2007, In : Journal of Statistical Physics. 129, 5-6, p. 949-1053 105 p.

Research output: Contribution to journalArticle

Universality
polynomials
Ensemble
eigenvalues
Orthogonal Polynomials

Universality in random matrix theory for orthogonal and symplectic ensembles

Deift, P. & Gioev, D., 2007, In : International Mathematics Research Papers. 2, 116 p., Art.IDrpm 004.

Research output: Contribution to journalArticle

2006

A model for the bus system in Cuernavaca (Mexico)

Baik, J., Borodin, A., Deift, P. & Suidan, T., Jul 14 2006, In : Journal of Physics A: Mathematical and General. 39, 28, p. 8965-8975 11 p., S11.

Research output: Contribution to journalArticle

Mexico
Random Matrices
Logarithmic Potential
potential theory
Potential Theory

A Riemann-Hilbert approach to some theorems on Toeplitz operators and orthogonal polynomials

Deift, P. & Östensson, J., Mar 2006, In : Journal of Approximation Theory. 139, 1-2, p. 144-171 28 p.

Research output: Contribution to journalArticle

Born approximation
Toeplitz Operator
Orthogonal Polynomials
Hilbert
Mathematical operators
2003

Long-Time Asymptotics for Solutions of the NLS Equation with Initial Data in a Weighted Sobolev Space

Deift, P. & Zhou, X., Aug 2003, In : Communications on Pure and Applied Mathematics. 56, 8, p. 1029-1077 49 p.

Research output: Contribution to journalArticle

NLS Equation
Long-time Asymptotics
Sobolev spaces
Weighted Sobolev Spaces

Products and ratios of characteristic polynomials of random Hermitlan matrices

Balk, J., Deift, P. & Strahov, E., Aug 1 2003, In : Journal of Mathematical Physics. 44, 8, p. 3657-3670 14 p.

Research output: Contribution to journalArticle

Hermitian matrix
Characteristic polynomial
Random Matrices
polynomials
products
2002

A priori Lp-estimates for solutions of Riemann-Hilbert problems

Deift, P. & Zhou, X., 2002, In : International Mathematics Research Notices. 40, p. 2121-2154 34 p.

Research output: Contribution to journalArticle

Lp Estimates
Riemann-Hilbert Problem

Fredholm Determinants, Jimbo-Miwa-Ueno τ-Functions, and Representation Theory

Borodin, A. & Deift, P., Sep 2002, In : Communications on Pure and Applied Mathematics. 55, 9, p. 1160-1230 71 p.

Research output: Contribution to journalArticle

Fredholm Determinant
Representation Theory
Riemann-Hilbert Problem
Unitary group
Operator

Perturbation theory for infinite-dimensional integrable systems on the line. A case study

Deift, P. & Zhou, X., 2002, In : Acta Mathematica. 188, 2, p. 163-262 100 p.

Research output: Contribution to journalArticle

Infinite-dimensional Systems
Integrable Systems
Perturbation Theory
Line
2001

A Fredholm determinant identity and the convergence of moments for random young tableaux

Baik, J., Deift, P. & Rains, E., Nov 2001, In : Communications in Mathematical Physics. 223, 3, p. 627-672 46 p.

Research output: Contribution to journalArticle

Fredholm Determinant
Young Tableaux
determinants
Moment
moments

A riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

Deift, P., Kriecherbauer, T., McLaughlin, K. R., Venakides, S. & Zhou, X., Aug 1 2001, In : Journal of Computational and Applied Mathematics. 133, 1-2, p. 47-63 17 p.

Research output: Contribution to journalArticle

Orthogonal Polynomials
Hilbert
Polynomials
Riemann-Hilbert Problem
Equilibrium Measure

Optimal tail estimates for directed last passage site percolation with geometric random variables

Baik, J., Deift, P., McLaughlin, K., Miller, P. & Zhou, X., Nov 2001, In : Advances in Theoretical and Mathematical Physics. 5, 6, p. 1-41 41 p.

Research output: Contribution to journalArticle

random variables
Tail
Random variable
estimates
Estimate
2000

Integrable systems and combinatorial theory

Deift, P., 2000, In : Notices of the American Mathematical Society. 47, 6, p. 631-640 Feature article.

Research output: Contribution to journalArticle

On the distribution of the length of the second row of a young diagram under plancherel measure

Baik, J., Deift, P. & Johansson, K., 2000, In : Geometric and Functional Analysis. 10, 4, p. 702-731 30 p.

Research output: Contribution to journalArticle

Plancherel Measure
Young Diagram
Tracy-Widom Distribution
Largest Eigenvalue
Random Matrices
1999

Integrable operators

Deift, P., 1999, In : American Mathematical Society Translations. 189, 2, p. 69-84

Research output: Contribution to journalArticle

Absolutely Continuous Spectrum
Transmission Coefficient
continuous spectra
Absolutely Continuous
A Priori Estimates

On the algebro-geometric integration of the Schlesinger equations

Deift, P., Its, A., Kapaev, A. & Zhou, X., 1999, In : Communications in Mathematical Physics. 203, 3, p. 613-633 21 p.

Research output: Contribution to journalArticle

Geometric Integration
Riemann Function
Riemann-Hilbert Problem
Theta Functions
Monodromy

On the distribution of the length of the longest increasing subsequence of random permutations

Baik, J., Deift, P. & Johansson, K., 1999, In : Journal of the American Mathematical Society. 12, 4, p. 1119-1178 60 p.

Research output: Contribution to journalArticle

Longest Increasing Subsequence
Steepest descent method
Steepest Descent Method
Random Permutation
Riemann-Hilbert Problem

Strong asymptotics of orthogonal polynomials with respect to exponential weights

Deift, P., Kriecherbauer, T., Mclaughlin, K. T. R., Venakides, S. & Zhou, X., Dec 1999, In : Communications on Pure and Applied Mathematics. 52, 12, p. 1491-1552 62 p.

Research output: Contribution to journalArticle

Exponential Weights
Orthogonal Polynomials
Polynomials
Coefficient
Riemann-Hilbert Problem

Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory

Deift, P., Kriecherbauer, T., McLaughlin, K. T. R., Venakides, S. & Zhou, X., Nov 1999, In : Communications on Pure and Applied Mathematics. 52, 11, p. 1335-1425 91 p.

Research output: Contribution to journalArticle

Exponential Weights
Uniform Asymptotics
Random Matrix Theory
Orthogonal Polynomials
Universality
1998

A continuum limit of the Toda Lattice

Deift, P. & McLaughlin, K. T. R., Jan 1998, In : Memoirs of the American Mathematical Society. 624, p. 1-216 216 p.

Research output: Contribution to journalArticle

Toda Lattice
Continuum Limit

New Results on the Equilibrium Measure for Logarithmic Potentials in the Presence of an External Field

Deift, P., Kriecherbauer, T. & McLaughlin, K. T. R., Dec 1998, In : Journal of Approximation Theory. 95, 3, p. 388-475 88 p.

Research output: Contribution to journalArticle

Korteweg-de Vries equation
Logarithmic Potential
Approximation theory
Equilibrium Measure
Mean field theory

Uniform asymptotics for orthogonal polynomials

Deift, P., Kriecherbauer, T., McLaughlin, K. T. R., Venakides, S. & Zhou, X., 1998, In : Documenta Mathematica. Extra volume III, p. 491-501

Research output: Contribution to journalArticle

1997
Matrix Models
Random Matrices
Statistical Mechanics
Hilbert
Statistical mechanics

Asymptotics for Polynomials Orthogonal with Respect to Varying Exponential Weights

Deift, P., Kriecherbauer, T., McLaughlin, K. T. R., Venakides, S. & Zhou, X., 1997, In : International Mathematics Research Notices. 16

Research output: Contribution to journalArticle

Exponential Weights
Orthogonal Polynomials
Integrable Systems
Nonlinear Schrödinger Equation
Line

New Results in Small Dispersion KdV by an Extension of the Steepest Descent Method for Riemann-Hilbert Problems

Deift, P., Venakides, S. & Zhou, X., 1997, In : International Mathematics Research Notices. 6, p. 284-299 16 p.

Research output: Contribution to journalArticle

Steepest Descent Method
Riemann-Hilbert Problem
Korteweg-de Vries Equation
1996

The toda rarefaction problem

Deift, P., Kamvissis, S., Kriecherbauer, T. & Zhou, X., Jan 1996, In : Communications on Pure and Applied Mathematics. 49, 1, p. 35-83 49 p.

Research output: Contribution to journalArticle

Pistons
Containers
Shock problems
Factorization
Gases