22 citations · 143 across the 51 of their papers we have counts for
5 papers · 1 filter
Spectral dimension of simple random walk on a long-range percolation cluster
Van Hao Can, David A. Croydon, Takashi Kumagai
Consider the long-range percolation model on the integer lattice in which all nearest-neighbour edges are present and otherwise and are connected with probab…
Biased random walk on supercritical percolation: Anomalous fluctuations in the ballistic regime
Adam M. Bowditch, David A. Croydon
We study biased random walk on the infinite connected component of supercritical percolation on the integer lattice for . For this model, Fribergh and Hammo…
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…
Scaling limit for random walk on the range of random walk in four dimensions
David A. Croydon, Daisuke Shiraishi
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 behavio…
On the stationary solutions of random polymer models and their zero-temperature limits
David A. Croydon, Makiko Sasada
We derive stationary measures for certain zero-temperature random polymer models, which we believe are new in the case of the zero-temperature limit of the beta random polymer (tha…