2018

Croydon, D. A. (2018) Scaling limits of stochastic processes associated with resistance forms. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 54 (4). pp. 1939-1968. doi:10.1214/17-AIHP861 ISSN 0246-0203.

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 ISSN 0178-8051.

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 ISSN 0002-9947. [ 🗎 Public].

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 ISSN 0091-1798.

2016

Croydon, David A. and Muirhead, Stephen (2016) Quenched localisation in the Bouchaud trap model with regularly varying traps. In: Stochastic Analysis on Large Scale Interacting Systems (SALSIS), Kyoto University, 26-29 Oct 2015. Published in: RIMS Kokyuroku Bessatsu, B59 pp. 305-320. ISSN 1881-6193.

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 ISSN 0091-1798. [ 🗎 Public].

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 ISSN 0304-4149.

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 ISSN 2052-4986. [ 🗎 Public].

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 ISSN 0178-8051. [ 🗎 Public].

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 ISSN 0178-8051. [ 🗎 Public].

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 ISSN 1083-6489. [ 🗎 Public].

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 ISSN 1663-4926. [ 🗎 Public].

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. ISSN 1083-6489. [ 🗎 Public].

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 ISSN 0001-8678.

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 ISSN 0022-4715. [ 🗎 Public].

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 ISSN 0091-1798. [ 🗎 Public].

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 ISSN 0246-0203.

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 ISSN 0926-2601.

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. ISSN 1083-6489. [ 🗎 Public].

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 ISSN 0304-4149.

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 ISSN 0178-8051.

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 ISSN 0001-8678.

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 ISSN 0024-6107.