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math.PR2026
Variance-Feedback Noise in Interacting Diffusions: Shape Dynamics and Mean-Field Limits
Ben Hambly, Vinh Nguyen
We study a system of attractive interacting diffusions where the variance feeds back into the noise. That is the common and idiosyncratic Brownian forcing has amplitude $κ(S_t^…
math.PR2026
A transform approach to the supercooled Stefan problem
Thomas Blore, Ben Hambly
We consider a generalisation of the probabilistic reformulation of the supercooled Stefan problem from arXiv:1902.05174 allowing for non-integrable initial data. From an applicatio…
math.PR2026
Probabilistic estimates for a system of noisy integrate-and-fire neurons
Ben Hambly, Aldaïr Petronilia, Christoph Reisinger +1
In this note, we establish various probabilistic estimates for an interacting particle system that describes the evolution of the membrane potentials in a network of excitatory int…