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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.PR2025
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…