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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