Biography
I am a Visiting Assistant Professor in the Department of Mathematics and Computer Science at the College of the Holy Cross. I completed my Ph.D. in Mathematics in May 2023 at the Courant Institute of Mathematical Sciences at NYU, where I was supported by a National Science Foundation Graduate Research Fellowship.
My current research interests are in probability and analysis, with a focus on models that arise from statistical mechanics and random matrix theory. I am particularly interested in Coulomb and Riesz gases, a class of singular interacting particle systems with a wide range of applications in random matrix theory, approximation theory, number theory and physics.
I also enjoy mentoring undergraduate research projects: if you are an undergraduate and are looking to learn more about conducting mathematics research, please feel free to email me!
Selected Publications and Preprints
L. Peilen. "On the Maximum of the Potential of a General Two-Dimensional Coulomb Gas." Electronic Communications in Probability, vol. 30, 2025, pp. 1-17. (link: https://projecteuclid.org/journals/electronic-communications-in-probability/volume-30/issue-none/On-the-maximum-of-the-potential-of-a-general-two/10.1214/25-ECP692.full)
L. Peilen. "Local Laws and a Mesoscopic CLT for β-Ensembles." Communications on Pure and Applied Mathematics, vol. 77, no. 4, 2024, pp. 2452-2567. (link: https://onlinelibrary.wiley.com/doi/10.1002/cpa.22175?af=R)
C. D. Guera, G. Lambert, L. Peilen. Mesoscopic transitions for β-ensembles at inter-
mediary temperature. arXiv:2609.25301, September 2026. (link: https://arxiv.org/pdf/2609.25301)
L. Peilen, S. Serfaty. "Local laws and fluctuations for super-Coulombic Riesz gases," with an appendix by X. Ros-Oton. arXiv: 2511.18623, December 2025. (link: https://arxiv.org/pdf/2511.18623)
D. Padilla-Garza, L. Peilen, E. Thoma. "Poisson Statistics for Coulomb Gases at Intermediate Temperature Regimes." arXiv: 2507.08198, July 2025. (link: https://arxiv.org/pdf/2507.08198)