Working Seminar on Mathematical Physics
of HSE University and Skoltech Igor Krichever Center for Advanced Studies
on Wednesdays at 16.20 at aud. 110 of the Faculty of Mathematics [ + zoom ]
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January 29, 2025 / Anton Rarovskii (Skoltech, HSE Univ.) |
March 26, 2025
Oleg Alekseev (Chebyshev Lab., S.-Petersburg State Univ.)
Stochastic Laplacian growth from a random matrix models perspective
Stochastic Laplacian growth is an important example for the nonlocal evolution of the plane curves, appearing in fluid dynamics, complex analysis, and probability theory. This talk explores stochastic Laplacian growth through the perspective of normal random matrices, providing a novel statistical interpretation of interface dynamics. We demonstrate that the partition function of the system serves as a tau-function of the dispersionless Toda hierarchy, while fluctuations around classical dynamics exhibit universal statistical properties independent of the initial domain. This work effectively bridges the gap between deterministic Laplacian growth and stochastic processes, offering a fresh perspective on long standing unsolved puzzles. The newly established relation between statistics of fluctuations and the circular Dyson ensemble (CUE), which also appears in studying Riemann zeta function, highlights an unexpected interdisciplinary connection