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math.PR2025
Asymptotic analysis of rare events in high dimensions
Anya Katsevich, Alexander Katsevich
Understanding rare events is critical across domains ranging from signal processing to reliability and structural safety, extreme-weather forecasting, and insurance. The analysis o…
math.PR2021
From local equilibrium to numerical PDE: Metropolis crystal surface dynamics in the rough scaling limit
Anya Katsevich
We derive the PDE governing the hydrodynamic limit of a Metropolis rate crystal surface height process in the "rough scaling" regime introduced by Marzuola and Weare. The PDE takes…
math.PR2021
The Local Equilibrium State of a Crystal Surface Jump Process in the Rough Scaling Regime
Anya Katsevich
We investigate the local equilibrium (LE) distribution of a crystal surface jump process as it approaches its hydrodynamic (continuum) limit in a nonstandard scaling regime introdu…