Research:
Since its inception, random matrix theory as grown into a field with a wide array of ramifications from operator algebra and free probability to integrable systems. My research revolves mainly around the questions of large deviations on the spectral quantities of such random matrices, that is the probabilities of rare events. To capture these phenomena for the largest eigenvalue for we can use spherical integrals as a proxy for the exponential of the largest eigenvalue, a technique incepted for general (non-Gaussian) random matrices in the first paper below.
List of publications:
- Alice Guionnet and J. H., Large deviations for the largest eigenvalue of Rademacher matrices, Ann. Probab. 48 (3) 1436 - 1465, May 2020.
- Fanny Augeri, Alice Guionnet, J.H., Large deviations for the largest eigenvalue of sub-Gaussian matrices, Commun. Math. Phys. 383, 997–1050 (2021).
- J.H., Large deviations for the largest eigenvalue of matrices with variance profiles, Electronic Journal of Probability, 27 :1 – 44, 2022.
- Nicholas Cook, Alice Guionnet and J.H., Spectrum and pseudospectrum for quadratic polynomials in Ginibre matrices, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 58(4) :2284 – 2320, 2022.
- Alice Guionnet and J. H., Asymptotics of k dimensional spherical integrals and applications, ALEA 2022, vol. 19, p. 769-797 .
- J.H., Asymptotic Behavior of Multiplicative Spherical Integrals and S-transform, arXiv:2108.11842, accepted in RMTA
- Justin Ko and J.H. Spherical Integrals of Sublinear Rank, arXiv:2208.03642, in revision for PTRF
- Benjamin McKenna and J. H., Large deviations for the largest eigenvalue of generalized sample covariance matrices, arXiv:2302.02847, Electronic Journal of Probabiliy, 29: 1-48 (2024).
- Raphaël Ducatez, Alice Guionnet, J.H, Large deviation principle for the largest eigenvalue of random matrices with a variance profile , arXiv:2403.05413.