Patrick Lopatto

Research Articles

1. Mobility Edge for the Anderson Model on the Bethe Lattice

   with A. Aggarwal

   (arXiv)

2. Maximum Gap in Complex Ginibre Matrices

   with M. Otto

   (arXiv)

3. Randomization-Based Confidence Sets for the Local Average Treatment Effect

   with P. M. Aronow and H. Chang

   (arXiv)

4. Smallest Gaps Between Eigenvalues of Real Gaussian Matrices

   with M. Meeker

   To appear in Bernoulli (arXiv)

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

   with P. Bourgade and O. Zeitouni

   Geometric and Functional Analysis 35, 2025 (arXiv)

6. Quenched Large Deviation Principles for Projections of ℓ_pⁿ Balls

   with K. Ramanan and X. Xie

   Journal of Functional Analysis 289 (6), 2025 (arXiv)

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

   with A. Goel and X. Xie

   Electronic Communications in Probability 29, 2024 (arXiv)

8. Fast Permutation Inference for Randomized Experiments With Binary Outcomes

   with P. M. Aronow and H. Chang

   To appear in Journal of Econometrics (arXiv)

9. Fluctuations in Quantum Unique Ergodicity at the Spectral Edge

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

   (arXiv)

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

    with A. Jagannath

    Communications in Mathematical Physics 405 (10), 2025 (arXiv)

11. Mobility Edge of Lévy Matrices

    with A. Aggarwal and C. Bordenave

    (arXiv)

12. Single Eigenvalue Fluctuations of General Wigner-Type Matrices

    with B. Landon and P. Sosoe

    Probability Theory and Related Fields 188 (1), 2024 (arXiv)

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

    with L. Benigni

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

14. Optimal Delocalization for Generalized Wigner Matrices

    with L. Benigni

    Advances in Mathematics 396, 2022 (arXiv)

15. Eigenvector Statistics of Lévy Matrices

    with A. Aggarwal and J. Marcinek

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

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

    with Z. Che

    Electronic Journal of Probability 26, 2021 (arXiv)

17. 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.

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

    with K. Luh

    Electronic Journal of Probability 26, 2021 (arXiv)

19. Comparison Theorem for Some Extremal Eigenvalue Statistics

    with B. Landon and J. Marcinek

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

20. Statistical Thresholds for Tensor PCA

    with A. Jagannath and L. Miolane

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

21. GOE Statistics for Lévy Matrices

    with A. Aggarwal and H.-T. Yau

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

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

    with Z. Che

    Electronic Journal of Probability 24, 2019 (arXiv)

23. 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)

24. Schatten-Class Truncated Toeplitz Operators

    with R. Rochberg

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

25. Formulas for Odd Zeta Values and Powers of π

    with M. Chamberland

    (arXiv)

    An earlier version appeared in the Journal of Integer Sequences (Article 11.2.5).