5 papers
Range convergence and sharp one-arm asymptotics for the critical percolation cluster in high dimensions
M. Cabezas, D. Croydon, A. Fribegh +2
For critical Bernoulli bond percolation on in the high-dimensional regime, we prove that the rescaled empirical measure of the cluster of the origin converges, in a suitable…
On the cover time of Brownian motion on the Brownian continuum random tree
George Andriopoulos, David A. Croydon, Vlad Margarint +1
Upon almost-every realisation of the Brownian continuum random tree (CRT), it is possible to define a canonical diffusion process or `Brownian motion'. The main result of this arti…
Collision properties of the four-dimensional random walk trace
David A. Croydon, Daisuke Shiraishi, Satomi Watanabe
We consider collisions of multiple random walks on the trace of a simple random walk on the four-dimensional integer lattice. For two independent walks (in continuous time), we app…
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…
Scaling limit for the cover time of the -biased random walk on a binary tree with
David A. Croydon
The -biased random walk on a binary tree of depth is the continuous-time Markov chain that has unit mean holding times and, when at a vertex other than the root or a leaf o…