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Paul Bourgade

Paul Bourgade

· Professor of Mathematics

New York University · Department of Mathematics

Active 1967–2025

h-index28
Citations2.5k
Papers10014 last 5y
Funding$673k

Academic metrics are sourced from OpenAlex and public funding records; values may differ from Google Scholar.

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About

Paul Bourgade is a Professor of Mathematics at NYU with research interests that include probability, random matrices, statistical physics, and stochastic processes. His work focuses on understanding complex systems through probabilistic models and mathematical physics, contributing to the theoretical foundations of these areas. As a faculty member at the Courant Institute, he engages in advanced research that intersects various domains of mathematics and physics, emphasizing the development of rigorous mathematical frameworks for phenomena involving randomness and statistical behavior.

Research topics

  • Combinatorics
  • Mathematics
  • Physics
  • Mathematical analysis
  • Quantum mechanics
  • Computer Science
  • Pure mathematics
  • Statistical physics
  • Mathematical physics
  • Statistics

Selected publications

  • Fixed Energy Universality for Generalized Wigner Matrices

    Communications on Pure and Applied Mathematics · 2015-12-15 · 100 citations

    article1st authorCorresponding

    Abstract We prove the Wigner‐Dyson‐Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.© 2016 Wiley Perio…

    PublisherDOI

  • The distribution of overlaps between eigenvectors of Ginibre matrices

    Probability Theory and Related Fields · 2019-11-14 · 59 citations

    articleOpen access1st authorCorresponding
    PublisherOA PDFDOI

  • Universality for a class of random band matrices

    Advances in Theoretical and Mathematical Physics · 2017-01-01 · 53 citations

    article1st authorCorresponding

    We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, $W\sim N$. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.

    PublisherDOI

  • The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem

    Apollo (University of Cambridge) · 2019-01-01 · 46 citations

    articleOpen access

    For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-κ}$ for some constant $κ> 0$. This expansion is based on approximating the Coulomb gas by a quasi-free Yukawa gas. Further, we prove that the fluctuations of the linear statistics are given by a Gaussian free field at any positive temperature. Our proof of this central limit theorem uses a loop equat…

    PublisherOA PDFDOI

  • Random Band Matrices in the Delocalized Phase I: Quantum Unique Ergodicity and Universality

    Communications on Pure and Applied Mathematics · 2020 · 41 citations

    1st authorCorresponding
    PublisherDOI

Recent grants

Frequent coauthors

  • Gérard Ben Arous

    New York University

    24 shared

  • Horng‐Tzer Yau

    Harvard University

    19 shared

  • Ashkan Nikeghbali

    18 shared

  • Alain Rouault

    Laboratoire de Mathématiques

    14 shared

  • Jun Yin

    12 shared

  • Louis‐Pierre Arguin

    9 shared

  • Marc Yor

    9 shared

  • László Erdős

    8 shared

Education

  • B.S., Mathematics and Physics

    École Polytechnique

    2006

  • M.S., Computer Science

    Telecom Paris

    2007

  • M.S., Probability

    Université Paris 6

    2007

  • Ph.D., Mathematics

    Université Paris 6

    2009

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