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Mathematics
USA
2026

D-Index & Metrics

Mathematics

D-Index
78
Citations
15842
World Ranking
175
National Ranking
101

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award
  • 2013 - Fellow of the American Mathematical Society
  • 2013 - Member of the National Academy of Sciences
  • 2001 - Fellow of the American Academy of Arts and Sciences

Overview

Horng-Tzer Yau is affiliated with Harvard University in the United States. Their research spans primarily across the field of Mathematics, with a particular focus on subfields such as Statistics and Probability, Mathematical Physics, Geometry and Topology, Discrete Mathematics and Combinatorics, and Condensed Matter Physics.

The main topics of their scholarly work include:

  • Random Matrices and Applications
  • Advanced Algebra and Geometry
  • Advanced Combinatorial Mathematics
  • Graph theory and applications
  • Stochastic processes and statistical mechanics
  • Spectral Theory in Mathematical Physics
  • Theoretical and Computational Physics

Some of their recent publications are as follows:

  • "Random Band Matrices in the Delocalized Phase I: Quantum Unique Ergodicity and Universality" (2020), published in Communications on Pure and Applied Mathematics
  • "Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős-Rényi graphs" (2020), published in The Annals of Probability
  • "Edge rigidity and universality of random regular graphs of intermediate degree" (2020), published in Geometric and Functional Analysis
  • "High Dimensional Normality of Noisy Eigenvectors" (2022), published in Communications in Mathematical Physics
  • "GOE statistics for Lévy matrices" (2021), published in Journal of the European Mathematical Society

Frequent collaborators in their work include:

  • Jiaoyang Huang
  • Changji Xu
  • Jun Yin
  • Christian Brennecke
  • Fan Yang

Their publications appear notably in venues such as:

  • arXiv (Cornell University)
  • Communications on Pure and Applied Mathematics
  • The Annals of Probability
  • Communications in Mathematical Physics
  • Geometric and Functional Analysis

Horng-Tzer Yau has been recognized by several professional awards. They were named Fellow of the American Academy of Arts and Sciences in 2001. In 2013, they were elected both as a Fellow of the American Mathematical Society and as a Member of the National Academy of Sciences.

Best Publications

  • Derivation of the Cubic Non-linear Schr"odinger Equation from Quantum Dynamics of Many-Body Systems

    Laszlo Erdos;Benjamin Schlein;Horng-Tzer Yau

  • Rigidity of eigenvalues of generalized Wigner matrices

    László Erdos;Horng-Tzer Yau;Jun Yin

  • The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics

    Elliott H. Lieb;Horng-Tzer Yau

  • Relative entropy and hydrodynamics of Ginzburg-Landau models

    Horng-Tzer Yau

  • Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate

    Laszlo Erdos;Benjamin Schlein;Horng-Tzer Yau

  • Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems

    László Erdős;Benjamin Schlein;Horng-Tzer Yau

  • Derivation of the nonlinear Schrödinger equation from a many body Coulomb system

    László Erdős;Horng-Tzer Yau

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

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

  • Bulk universality for generalized Wigner matrices

    László Erdős;Horng-Tzer Yau;Jun Yin

  • Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices

    László Erdős;Benjamin Schlein;Horng-Tzer Yau

  • The stability and instability of relativistic matter

    Elliott H. Lieb;Horng Tzer Yau

  • Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation

    László Erdős;Horng-Tzer Yau

  • Local Semicircle Law and Complete Delocalization for Wigner Random Matrices

    László Erdős;Benjamin Schlein;Horng-Tzer Yau

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

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

  • Bulk Universality for Wigner Matrices

    Laszlo Erdos;Sandrine Péché;José A. Ramírez;Benjamin Schlein

  • Universality of random matrices and local relaxation flow

    László Erdős;Benjamin Schlein;Horng-Tzer Yau

  • Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential

    László Erdos;Benjamin Schlein;Horng-Tzer Yau

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

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

  • Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics

    Sheng Lin Lu;Horng-Tzer Yau

  • Local semicircle law and complete delocalization for Wigner random matrices

    Laszlo Erdos;Benjamin Schlein;Horng-Tzer Yau

  • Rigorous derivation of the Gross-Pitaevskii equation.

    Laszlo Erdos;Benjamin Schlein;Horng-Tzer Yau

  • A Dynamical Approach to Random Matrix Theory

    László Erdős;Horng-Tzer Yau

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

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

Frequent Co-Authors

Benjamin Schlein
Benjamin Schlein University of Zurich
László Erdős
László Erdős Institute of Science and Technology Austria
Antti Knowles
Antti Knowles University of Geneva
Claudio Landim
Claudio Landim Instituto Nacional de Matemática Pura e Aplicada
Elliott H. Lieb
Elliott H. Lieb Princeton University
Bruno Nachtergaele
Bruno Nachtergaele University of California, Davis
Stefano Olla
Stefano Olla Paris Dauphine University
Jeremy Quastel
Jeremy Quastel University of Toronto
Terence Tao
Terence Tao University of California, Los Angeles

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