2 citations · 3 across the 5 of their papers we have counts for
5 papers
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…
Heat kernel fluctuations for stochastic processes on fractals and random media
Sebastian Andres, David Croydon, Takashi Kumagai
It is well-known that stochastic processes on fractal spaces or in certain random media exhibit anomalous heat kernel behaviour. One manifestation of such irregular behaviour is th…
Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model
Sebastian Andres, David A. Croydon, Takashi Kumagai
We present on-diagonal heat kernel estimates and quantitative homogenization statements for the one-dimensional Bouchaud trap model. The heat kernel estimates are obtained using st…
Quenched and averaged tails of the heat kernel of the two-dimensional uniform spanning tree
Martin T. Barlow, David A. Croydon, Takashi Kumagai
This article investigates the heat kernel of the two-dimensional uniform spanning tree. We improve previous work by demonstrating the occurrence of log-logarithmic fluctuations aro…
Time-changes of stochastic processes associated with resistance forms
D. A. Croydon, B. M. Hambly, T. Kumagai
Given a sequence of resistance forms that converges with respect to the Gromov-Hausdorff-vague topology and satisfies a uniform volume doubling condition, we show the convergence o…