2017

Croydon, David A. and Muirhead, Stephen (2017) Quenched localisation in the Bouchaud trap model with slowly varying traps. Probability Theory and Related Fields, 168 (1-2). pp. 269-315. doi:10.1007/s00440-016-0710-8

Charmoy, Philippe H. A., Croydon, David A. and Hambly, Ben M. (2017) Central limit theorems for the spectra of classes of random fractals. Transactions of the American Mathematical Society, 369 . 8967-9013 . doi:10.1090/tran/7147

Barlow, Martin T., Croydon, David A. and Kumagai, Takashi (2017) Subsequential scaling limits of simple random walk on the two-dimensional uniform spanning tree. Annals of Probability, 45 (1). pp. 4-55. doi:10.1214/15-AOP1030

2016

Croydon, David A. and Muirhead, Stephen (2016) Quenched localisation in the Bouchaud trap model with regularly varying traps. RIMS Kokyuroku Bessatsu . (In Press)

2015

Chen, Zhen-Qing, Croydon, David A. and Kumagai, Takashi (2015) Quenched invariance principles for random walks and elliptic diffusions in random media with boundary. The Annals of Probability, 43 (4). pp. 1594-1642. doi:10.1214/14-AOP914

Croydon, David A. and Muirhead, Stephen (2015) Functional limit theorems for the Bouchaud trap model with slowly-varying traps. Stochastic Processes and their Applications, 125 (5). pp. 1980-2009. doi:10.1016/j.spa.2014.12.004

Croydon, David A. (2015) Moduli of continuity of local times of random walks on graphs in terms of the resistance metric. Transactions of the London Mathematical Society, Volume 2 (Number 1). pp. 57-79. doi: 10.1112/tlms/tlv003

2013

Croydon, David A. (2013) Slow movement of a random walk on the range of a random walk in the presence of an external field. Probability Theory and Related Fields, Volume 157 (Number 3-4). pp. 515-534. doi:10.1007/s00440-012-0463-y

Croydon, David A., Fribergh, A. and Kumagai, T. (Takashi) (2013) Biased random walk on critical Galton–Watson trees conditioned to survive. Probability Theory and Related Fields, Volume 157 (Number 1-2). pp. 453-507. doi:10.1007/s00440-012-0462-z

2012

Croydon, David A., Hambly, Ben M. and Kumagai, Takashi (2012) Convergence of mixing times for sequences of random walks on finite graphs. Electronic Journal of Probability, Vol.17 . article no.3. doi:10.1214/EJP.v17-1705

Croydon, David A. (2012) Scaling limit for the random walk on the largest connected component of the critical random graph. Research Institute for Mathematical Sciences. Publications, Vol.48 (No.2). pp. 279-338. doi:10.2977/PRIMS/70

2010

Croydon, David A. and Hambly, Ben M. (2010) Spectral asymptotics for stable trees. Electronic Journal of Probability, Vol.15 (No.57). pp. 1772-1801.

Croydon, David A. (2010) Scaling limits for simple random walks on random ordered graph trees. Advances in Applied Probability, Vol.42 (No.2). pp. 528-558. doi:10.1239/aap/1275055241

2009

Croydon, David A. (2009) Random walk on the range of random walk. Journal of Statistical Physics, Vol.136 (No.2). pp. 349-372. doi:10.1007/s10955-009-9785-2

Croydon, David A. (2009) Hausdorff measure of arcs and Brownian motion on Brownian spatial trees. Annals of Probability, Vol.37 (No.3). pp. 946-978. doi:10.1214/08-AOP425

2008

Croydon, David A. (2008) Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random tree. Annales de l'Institut Henri Poincaré (B). Probabilites et Statistiques, Vol.44 (No.6). pp. 987-1019. doi:10.1214/07-AIHP153

Croydon, David A. and Hambly, Ben M. (2008) Local limit theorems for sequences of simple random walks on graphs. Potential Analysis, Vol.29 (No.4). pp. 351-389. doi:10.1007/s11118-008-9101-9

Croydon, David A. and Kumagai, Takashi (2008) Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive. Electronic Journal of Probability, Vol.13 . pp. 1419-1441.

Croydon, David A. and Hambly, Ben M. (2008) Self-similarity and spectral asymptotics for the continuum random tree. Stochastic Processes and their Applications, Vol.118 (No.5). pp. 730-754. doi:10.1016/j.spa.2007.06.005

Croydon, David A. (2008) Volume growth and heat kernel estimates for the continuum random tree. Probability Theory and Related Fields, Vol.140 (No.1-2). pp. 207-238. doi:10.1007/s00440-007-0063-4

2007

Croydon, David A. (2007) The Hausdorff dimension of a class of random self-similar fractal trees. Advances in Applied Probability, Vol.39 (No.3). pp. 708-730. doi:10.1239/aap/1189518635

Croydon, David A. (2007) Heat kernel fluctuations for a resistance form with non-uniform volume growth. Proceedings of the London Mathematical Society, Vol.94 (No.3). pp. 672-694. doi:10.1112/plms/pdl025