Spectral dimension of simple random walk on a long-range percolation cluster
VH Can, DA Croydon, T Kumagai - Electronic Journal of …, 2022 - projecteuclid.org
Consider the long-range percolation model on the integer lattice Z d in which all nearest-
neighbour edges are present and otherwise x and y are connected with probability qx, y …
neighbour edges are present and otherwise x and y are connected with probability qx, y …
Scaling limit for random walk on the range of random walk in four dimensions
DA Croydon, D Shiraishi - Annales de l'Institut Henri Poincare (B) …, 2023 - projecteuclid.org
We establish scaling limits for the random walk whose state space is the range of a simple
random walk on the four-dimensional integer lattice. These concern the asymptotic …
random walk on the four-dimensional integer lattice. These concern the asymptotic …
Aging and sub-aging for one-dimensional random walks amongst random conductances
DA Croydon, D Kious, C Scali - arXiv preprint arXiv:2308.02230, 2023 - arxiv.org
We consider random walks amongst random conductances in the cases where the
conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the …
conductances can be arbitrarily small, with a heavy-tailed distribution at 0, and where the …
Extremal regime for one-dimensional Mott variable-range hopping
DA Croydon, R Fukushima, S Junk - arXiv preprint arXiv:2208.12102, 2022 - arxiv.org
We study the asymptotic behaviour of a version of the one-dimensional Mott random walk in
a regime that exhibits severe blocking. We establish that, for any fixed time, the appropriately …
a regime that exhibits severe blocking. We establish that, for any fixed time, the appropriately …