3 papers
math.PR2025
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…
math.PR2025
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…
math.PR2024
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…