22 citations · 143 across the 51 of their papers we have counts for
10 papers · 1 filter
Random walk on the range of random walk
David A. Croydon
We study the random walk on the range of a simple random walk on in dimensions . When we establish quenched and annealed scaling limits for th…
Local limit theorems for sequences of simple random walks on graphs
D. A. Croydon, B. M. Hambly
In this article, local limit theorems for sequences of simple random walks on graphs are established. The results formulated are motivated by a variety of random graph models, and…
Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive
David A. Croydon, Takashi Kumagai
We establish a variety of properties of the discrete time simple random walk on a Galton-Watson tree conditioned to survive when the offspring distribution, say, is in the doma…
Self-similarity and spectral asymptotics for the continuum random tree
D. A. Croydon, B. M. Hambly
We use the random self-similarity of the continuum random tree to show that it is homeomorphic to a post-critically finite self-similar fractal equipped with a random self-similar…
Scaling limits for simple random walks on random ordered graph trees
David A. Croydon
Consider a family of random ordered graph trees , where has vertices. It has previously been established that if the associated search-depth processes co…
Scaling limit for the random walk on the largest connected component of the critical random graph
David A. Croydon
A scaling limit for the simple random walk on the largest connected component of the Erdos-Renyi random graph in the critical window is deduced. The limiting diffusion is construct…