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Mathematics

D-Index
35
Citations
4771
World Ranking
2794
National Ranking
50

Overview

Antti Knowles is a researcher affiliated with the University of Geneva in Switzerland, specializing in fields related to mathematics and physics. Their primary field of study is Mathematics, with a focus on subfields including Mathematical Physics, Statistics and Probability, Geometry and Topology, Atomic and Molecular Physics, and Condensed Matter Physics.

Their research covers a range of topics, notably:

  • Random Matrices and Applications
  • Spectral Theory in Mathematical Physics
  • Graph theory and applications
  • Stochastic processes and statistical mechanics
  • Theoretical and Computational Physics
  • Complex Systems and Time Series Analysis
  • Cold Atom Physics and Bose-Einstein Condensates

Knowles has contributed to numerous academic publications, with a record of papers produced in a variety of scientific journals. Frequent publication venues include:

  • arXiv (Cornell University)
  • The Annals of Probability
  • Communications in Mathematical Physics
  • Annales de l Institut Henri Poincaré Probabilités et Statistiques
  • Geometric and Functional Analysis

Among their recent papers are notable works such as:

  • "Spectral radii of sparse random matrices" (2020), published in Annales de l Institut Henri Poincaré Probabilités et Statistiques
  • "Extremal eigenvalues of critical Erdős-Rényi graphs" (2021), published in The Annals of Probability
  • "Edge rigidity and universality of random regular graphs of intermediate degree" (2020), published in Geometric and Functional Analysis
  • "Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs" (2021), published in Probability Theory and Related Fields
  • "The mean-field limit of quantum Bose gases at positive temperature" (2021), published in Journal of the American Mathematical Society

Knowles often collaborates with other researchers. Frequent coauthors include:

  • Johannes Alt
  • Raphaël Ducatez
  • Jürg Fröhlich
  • Benjamin Schlein
  • Vedran Sohinger

Best Publications

  • Spectral statistics of Erdős–Rényi graphs I: Local semicircle law

    László Erdős;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • Spectral Statistics of Erdős-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues

    László Erdős;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • Spectral statistics of Erd\H{o}s-R'{e}nyi graphs I: Local semicircle law

    László Erdős;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • The local semicircle law for a general class of random matrices

    László Erdős;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • Mean-Field Dynamics: Singular Potentials and Rate of Convergence

    Antti Knowles;Peter Pickl

  • The Isotropic Semicircle Law and Deformation of Wigner Matrices

    Antti Knowles;Jun Yin

  • Anisotropic local laws for random matrices

    Antti Knowles;Jun Yin

  • On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

    Jürg Fröhlich;Antti Knowles;Simon Schwarz

  • Isotropic local laws for sample covariance and generalized Wigner matrices

    Bloemendal Alex;László Erdős;Antti Knowles;Horng-Tzer Yau

  • On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

    Juerg Froehlich;Antti Knowles;Simon Schwarz

  • Spectral Statistics of Erd{\H o}s-R'enyi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues

    Laszlo Erdos;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • On the principal components of sample covariance matrices

    Alex Bloemendal;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • Eigenvector Distribution of Wigner Matrices

    Antti Knowles;Jun Yin

  • Local Semicircle Law for Random Regular Graphs

    Roland Bauerschmidt;Antti Knowles;Horng-Tzer Yau

  • Delocalization and Diffusion Profile for Random Band Matrices

    László Erdős;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • Delocalization and Diffusion Profile for Random Band Matrices

    Laszlo Erdos;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • Atomism and quantization

    J Fröhlich;A Knowles;A Pizzo

  • Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

    Laszlo Erdos;Antti Knowles

  • Averaging Fluctuations in Resolvents of Random Band Matrices

    Laszlo Erdos;Antti Knowles;Horng-Tzer Yau

  • Averaging Fluctuations in Resolvents of Random Band Matrices

    László Erdős;Antti Knowles;Horng-Tzer Yau

  • Lectures on the local semicircle law for Wigner matrices

    Florent Benaych-Georges;Antti Knowles

  • The Local Semicircle Law for a General Class of Random Matrices

    Laszlo Erdos;Antti Knowles;Horng-Tzer Yau;Jun Yin

  • Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices

    Alex Bloemendal;Laszlo Erdos;Antti Knowles;Horng-Tzer Yau

Frequent Co-Authors

Horng-Tzer Yau
Horng-Tzer Yau Harvard University
László Erdős
László Erdős Institute of Science and Technology Austria
Benjamin Schlein
Benjamin Schlein University of Zurich
Charles Bordenave
Charles Bordenave Aix-Marseille University

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