From the 1 of 8 linked papers with an AI index.
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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…
Particle Systems and McKean--Vlasov Dynamics with Singular Interaction through Local Times
Graeme Baker, Ben Hambly, Philipp Jettkant
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all th…
Control of McKean--Vlasov SDEs with Contagion Through Killing at a State-Dependent Intensity
Ben Hambly, Philipp Jettkant
We consider a novel McKean--Vlasov control problem with contagion through killing of particles and common noise. Each particle is killed at an exponential rate according to an inte…
Scaling limit for Brownian motions on the -level Sierpinski gaskets: The fractal to Euclidean crossover
David A. Croydon, Ben Hambly, Takashi Kumagai
In two dimensions, the -level Sierpinski gasket is obtained by splitting an equilateral triangle into a collection of equilateral triangles of equal size…
Particle systems and the supercooled Stefan problem with non-integrable initial data
Thomas Blore, D. G. M Flynn, Ben Hambly
We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of…
Non-negative Martingale Solutions to the Stochastic Porous Medium Equation with Sticky Behavior
Ben Hambly, Dörte Kreher, Konstantins Starovoitovs
We construct non-negative martingale solutions to the stochastic porous medium equation in one dimension with homogeneous Dirichlet boundary conditions which exhibit a type of stic…