Research
My research interests are in random matrix theory, random graphs, random polynomials, point processes and related areas of probability and analysis.
Papers and preprints
A. Campbell, G. Cipolloni, L. Erdős, and H.C. Ji, On the spectral edge of non-Hermitian random matrices. Preprint available at arxiv.org/abs/2404.17512.
A. Campbell, S. O’Rourke, and D.Renfrew, The fractional free convolution of R-diagonal operators and random polynomials under repeated differentiation. International Mathematics Research Notices (2024). Available open access on Oxford Academic.
A. Campbell, K. Luh, V. Margarint, Rate of Convergence in Multiple SLE using Random Matrix Theory. Preprint available at arxiv.org/abs/2301.04722.
A. Campbell, K. Luh, and S. O’Rourke, Extreme eigenvalues of Laplacian random matrices with Gaussian entries. With an appendix by S. Arenas-Velilla and V. Pérez-Abreu. Preprint available at arxiv.org/abs/2211.17175.
A. Campbell, S. O’Rourke, Spectrum of Lévy–Khintchine Random Laplacian Matrices. Journal of Theoretical Probability, (2023). Available open access from Springer.
A. Campbell, S. O’Rourke, Spectrum of heavy-tailed elliptic random matrices, Electronic Journal of Probability, Vol 27, 1-56 (2022), available at arxiv.org/abs/2010.01261.
Invited Talks
MAA Rocky Mountain Section Meeting session on Random Matrices and Free Probability Theory, April 19-20 2024, Colorado College
Probability Seminar, April 18 2024, University of Colorado Boulder
Bielefeld-Melbourne-Seoul Random Matrix Seminar, March 13 2024, online
Probability Seminar (Oberseminar Stochastik), November 29 2023, Universität Münster
UC Berkeley Probabilistic Operator Algebra Seminar, online, August 14 2023
Workshop on Random Matrices and Random Polynomials at UIC, May 15-16 2023
Stochastics Seminar, April 13 2023, Georgia Institute of Technology
Mathematical Physics & Analysis Seminar, January 12 2023, IST Austria
Joint Mathematics Meetings, online, April 6-9 2022, AMS Special Session on Random Matrix Theory and its Applications
Other Talks
Math for All in Boulder, Boulder Colorado, February 25 2023
Joint Mathematics Meetings, Boston, January 6, 2023, AMS Contributed Paper Session on Probability Theory and Stochastic Processes
Summer School on Free Probability, Random Matrices, and Applications, University of Wyoming, June 6–10, 2022 Video
Math for All in New Orleans, online, February 4-6 2022