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math.PR2026
An Autonomous Spectral Representation for Fully Asymmetric Spherical Sherrington-Kirkpatrick Dynamics
James MacLaurin, Pedro Vilanova
We study the large size dynamics of a fully asymmetric spherical Sherrington- Kirkpatrick model, allowing for a distinguished random signal that interacts with the evolving spin co…
math.PR2025
The Kinetic Limit of Balanced Neural Networks
James MacLaurin, Pedro Vilanova
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that…
math.PR2024
Large Deviations of Piecewise-Deterministic-Markov-Processes with Application to Stochastic Calcium Waves
Gaetan Barbet, James MacLaurin, Moshe Silverstein
We prove a Large Deviation Principle for Piecewise Deterministic Markov Processes (PDMPs). This is an asymptotic estimate for the probability of a trajectory in the large size limi…