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Percy Deift

Silver Professor; Professor of Mathematics

    1973 …2019
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    Research Output 1973 2019

    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

    Universality in numerical computation with random data: Case Studies, Analytical Results and Some Speculations

    Deift, P. & Trogdon, T., Jan 1 2018, Computation and Combinatorics in Dynamics, Stochastics and Control - The Abel Symposium. Di Nunno, G., Celledoni, E., Ebrahimi-Fard, K. & Munthe-Kaas, H. Z. (eds.). Springer Heidelberg, Vol. 13. p. 221-231 11 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Speculation
    Numerical Computation
    Universality
    Observation
    Standards
    2017

    On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II

    Bothner, T., Deift, P., Its, A. & Krasovsky, I., 2017, Operator Theory: Advances and Applications. Springer International Publishing, Vol. 259. p. 213-234 22 p. (Operator Theory: Advances and Applications; vol. 259).

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Scaling Limit
    Asymptotic Behavior
    Trace Class Operators
    Proposition
    Determinant
    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

    How long does it take to computer the eigenvalues of a random symmetric matrix?

    Deift, P., Menon, G. & Phrang, C., 2014, Random matrix theory, interacting particle systems and integrable systems. Deift, P. & Forrester, P. (eds.). New York: Cambridge University Press, p. 411-442 (MSRI Publications; vol. 65).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    On the asymptotics of a Toeplitz determinant with singularities

    Deift, P., Its, A. & Krasovsky, I., 2014, Random matrix theory, interacting particle systems and integrable systems. Deift, P. & Forrester, P. (eds.). New York: Cambridge University Press, Vol. 65. p. 93-146 (MSRI Publications).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    Random matrix theory, interacting particle systems, and integrable systems

    Deift, P. (ed.) & Forrester, P. (ed.), 2014, New York (N.Y.): Cambridge University Press. 528 p. (Mathematical Sciences Research Institute publications; vol. 65)

    Research output: Book/ReportBook

    Special issue on Painleve equations, part 1

    Deift, P. (ed.) & Its, A. (ed.), Feb 2014, In : Constructive Approximation. 39, 1

    Research output: Contribution to journalSpecial issue

    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
    2009

    Random matrix theory: Invariant ensembles and universality

    Deift, P. & Gioev, D., 2009, Courant Lecture Notes 18. Providence, Rhode Island: American Mathematical Society

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    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

    Some open problems in random matrix theory and the theory of integrable systems

    Deift, P., 2008, Integrable systems and random matrices. Baik, J., Kriecherbauer, T., Li, L-C., McLaughlin, K. T-R. & Tomei, C. (eds.). Providence, Rhode Island: AMS, p. 419-430 (Contemporary Mathematics 458).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    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

    Riemann-Hilbert methods in the theory of orthogonal polynomials

    Deift, P., 2007, Spectral theory and mathematical physics: A festschrift in honor of Barry Simon's 60th birthday. Gesztesy, F., Deift, P., Galvez, C., Perry, P. & Schlag, W. (eds.). Providence, Rhode Island: AMS, p. 715-740 (Proceedings of Symposia in Pure Mathematics; vol. 76).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    Spectral theory and mathematical physics: A festschrift in honor of Barry Simon's 60th birthday

    Deift, P. (ed.), Gesztesy, F. (ed.), Galvez, C. (ed.), Perry, P. (ed.) & Schlag, W. (ed.), 2007, Providence (R.I.): American Mathematical Society. 948 p. (Proceedings of symposia in pure mathematics; vol. 76/2)

    Research output: Book/ReportBook

    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

    Universality for mathematical and physical systems

    Deift, P., 2006, International Congress of Mathematicians, ICM 2006. Vol. 1. p. 125-152 28 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Universality
    Thermodynamics
    Solitaire
    Riemann hypothesis
    Neutron
    2005

    Random matrix theory IV (analytical methods)

    Deift, P. & Zhou, X., 2005, Encyclopedia of Nonlinear Science. Scott, A. (ed.). New York and London: Routledge, p. 771-774

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    Riemann-Hilbert problem

    Deift, P. & Zhou, X., 2005, Encyclopedia of Nonlinear Science. Scott, A. (ed.). New York and London: Routledge, p. 804-808

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    2003

    Four lectures on random matrix theory

    Deift, P., 2003, Asymptotic combinatorics with applications to mathematical physics (St. Petersburg, 2001). Berlin: Springer, p. 21-52 (Lecture Notes in Mathematics; vol. 1815).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    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

    Asymptotics for oscillatory Riemann-Hilbert problems

    Deift, P. & Zhou, X., 1999, CCAST Proceedings: Four lectures at MSRI, Berkeley, January 19-23, 1999 and CCAST, Beijing, May 3-7, 1999.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution