Patrick Lopatto

Research Articles

1. Uniqueness of the Mobility Edge for Lévy Matrices

   (CDR)

2. Maximum Cut and Maximum Bisection in Random Regular Graphs

   with P. M. Aronow

   (arXiv)

3. Overlap Structure of Mixed Even p-Spin Models

   with P. M. Aronow

   (arXiv)

4. Parisi Measure of the Sherrington–Kirkpatrick Model with External Field

   (CDR)

5. A Positive Resolution of the Gap-Entropy Conjecture

   with P. M. Aronow and N. Kallus

   (arXiv)

6. Quantitative Parisi Formulas and Fluctuations in the Sherrington-Kirkpatrick Model

   with P. M. Aronow

   (arXiv)

7. Optimal Central Limit Theorem for Bounded Random Variables in High Dimensions

   with P. M. Aronow

   (arXiv)

8. Replica Symmetry Breaking at Arbitrary Depth

   with P. M. Aronow

   (arXiv)

9. Adaptive Confidence Sets for Binary Regression without Design Smoothness

   with P. M. Aronow

   (arXiv)

10. Nearly-Minimax Variance Estimation under Rough Random Design

    with P. M. Aronow

    (arXiv)

11. Full Replica Symmetry Breaking in the Sherrington-Kirkpatrick Model

    (arXiv)

12. Quantitative Eigenvector Universality for Generalized Wigner Matrices

    with L. Benigni

    (arXiv)

13. Sobolev Convergence of Log-Determinants for Smooth Wigner Matrices

    with G. Cipolloni

    (arXiv)

14. Minimax Unbiased Estimation for Finite Populations with Bounded Outcomes

    with P. M. Aronow

    (arXiv)

15. Replica Symmetry up to the de Almeida-Thouless Line in the Sherrington-Kirkpatrick Model

    (arXiv)

16. One-Step TMLE for Weighted Average Treatment Effects

    with Y. Liu and I. Malenica

    (arXiv)

17. Mobility Edge for the Anderson Model on Random Regular Graphs

    with S. Liu

    (arXiv)

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

    with A. Aggarwal

    (arXiv)

19. Maximum Gap in Complex Ginibre Matrices

    with M. Otto

    (arXiv)

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

    with P. M. Aronow and H. Chang

    (arXiv)

21. Smallest Gaps Between Eigenvalues of Real Gaussian Matrices

    with M. Meeker

    To appear in Bernoulli (arXiv)

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

    with P. Bourgade and O. Zeitouni

    Geometric and Functional Analysis 35, 2025 (arXiv)

23. Quenched Large Deviation Principles for Projections of ℓ_pⁿ Balls

    with K. Ramanan and X. Xie

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

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

    with A. Goel and X. Xie

    Electronic Communications in Probability 29, 2024 (arXiv)

25. Fast Permutation Inference for Randomized Experiments With Binary Outcomes

    with P. M. Aronow and H. Chang

    To appear in Journal of Econometrics (arXiv)

26. Fluctuations in Quantum Unique Ergodicity at the Spectral Edge

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

    (arXiv)

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

    with A. Jagannath

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

28. Mobility Edge of Lévy Matrices

    with A. Aggarwal and C. Bordenave

    (arXiv)

29. Single Eigenvalue Fluctuations of General Wigner-Type Matrices

    with B. Landon and P. Sosoe

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

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

    with L. Benigni

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

31. Optimal Delocalization for Generalized Wigner Matrices

    with L. Benigni

    Advances in Mathematics 396, 2022 (arXiv)

32. Eigenvector Statistics of Lévy Matrices

    with A. Aggarwal and J. Marcinek

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

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

    with Z. Che

    Electronic Journal of Probability 26, 2021 (arXiv)

34. 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.

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

    with K. Luh

    Electronic Journal of Probability 26, 2021 (arXiv)

36. Comparison Theorem for Some Extremal Eigenvalue Statistics

    with B. Landon and J. Marcinek

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

37. Statistical Thresholds for Tensor PCA

    with A. Jagannath and L. Miolane

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

38. GOE Statistics for Lévy Matrices

    with A. Aggarwal and H.-T. Yau

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

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

    with Z. Che

    Electronic Journal of Probability 24, 2019 (arXiv)

40. 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)

41. Schatten-Class Truncated Toeplitz Operators

    with R. Rochberg

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

42. 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).