Patrick Lopatto

Research Articles

1. Smallest Gaps Between Eigenvalues of Real Gaussian Matrices

   with M. Meeker

   (arXiv)

2. Optimal Rigidity and Maximum of the Characteristic Polynomial of Wigner Matrices

   with P. Bourgade and O. Zeitouni

   (arXiv)

3. Quenched Large Deviation Principles for Projections of ℓ_pⁿ Balls

   with K. Ramanan and X. Xie

   (arXiv)

4. Central Limit Theorem for the Complex Eigenvalues of Gaussian Random Matrices

   with A. Goel and X. Xie

   (arXiv)

5. Fast Permutation Inference for Randomized Experiments With Binary Outcomes

   with P. M. Aronow and H. Chang

   (arXiv)

6. Fluctuations in Quantum Unique Ergodicity at the Spectral Edge

   with L. Benigni, N. Chen, and X. Xie

   (arXiv)

7. Existence of the Free Energy for Heavy-Tailed Spin Glasses

   with A. Jagannath

   (arXiv)

8. Mobility Edge of Lévy Matrices

   with A. Aggarwal and C. Bordenave

   (arXiv)

9. Single Eigenvalue Fluctuations of General Wigner-Type Matrices

   with B. Landon and P. Sosoe

   Probability Theory and Related Fields 2023 (arXiv)

10. Fluctuations in Local Quantum Unique Ergodicity for Generalized Wigner Matrices

    with L. Benigni

    Communications in Mathematical Physics 391 (2), 2022 (arXiv)

11. Optimal Delocalization for Generalized Wigner Matrices

    with L. Benigni

    Advances in Mathematics 396, 2022 (arXiv)

12. Eigenvector Statistics of Lévy Matrices

    with A. Aggarwal and J. Marcinek

    Annals of Probability 49 (4), 2021 (arXiv)

13. Universality of the Least Singular Value for the Sum of Random Matrices

    with Z. Che

    Electronic Journal of Probability 26, 2021 (arXiv)

14. An Improved Lower Bound for Sparse Reconstruction from Subsampled Walsh Matrices

    with J. Błasiok, K. Luh, J. Marcinek, and S. Rao

    Discrete Analysis 2023:3 (arXiv)

    A preliminary version appeared in FOCS 2019.

15. Tail Bounds for Gaps Between Eigenvalues of Sparse Random Matrices

    with K. Luh

    Electronic Journal of Probability 26, 2021 (arXiv)

16. Comparison Theorem for Some Extremal Eigenvalue Statistics

    with B. Landon and J. Marcinek

    Annals of Probability 48 (6), 2020 (arXiv)

17. Statistical Thresholds for Tensor PCA

    with A. Jagannath and L. Miolane

    Annals of Applied Probability 30 (4), 2020 (arXiv)

18. GOE Statistics for Lévy Matrices

    with A. Aggarwal and H.-T. Yau

    Journal of the European Mathematical Society, 23 (11), 2021 (arXiv)

19. Universality of the Least Singular Value for Sparse Random Matrices

    with Z. Che

    Electronic Journal of Probability 24, 2019 (arXiv)

20. Simplicial Abel–Jacobi Maps and Reciprocity Laws

    with M. Kerr and J. Lewis, and an appendix by J. I. Burgos-Gil

    Journal of Algebraic Geometry 27 (1), 2018 (arXiv)

21. Schatten-Class Truncated Toeplitz Operators

    with R. Rochberg

    Proceedings of the American Mathematical Society 144 (2), 2016 (arXiv)

22. Formulas for Odd Zeta Values and Powers of π

    with M. Chamberland

    Journal of Integer Sequences 14 (2), 2011 (arXiv)