2017

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 . ISSN 0002-9947 (In Press)

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. ISSN 0091-1798

2016

Croydon, David A. and Muirhead, Stephen. (2016) Quenched localisation in the Bouchaud trap model with regularly varying traps. RIMS Kokyuroku Bessatsu . ISSN 1881-6193 (In Press)

Croydon, David A. and Muirhead, Stephen. (2016) Quenched localisation in the Bouchaud trap model with slowly varying traps. Probability Theory and Related Fields . ISSN 0178-8051 (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. ISSN 0091-1798

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. 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. ISSN 2052-4986

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. ISSN 0178-8051

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. ISSN 0178-8051

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. ISSN 1083-6489

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. ISSN 1663-4926

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

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. 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. ISSN 0022-4715

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. ISSN 0091-1798

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. 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. 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

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. 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. 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. 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. ISSN 0024-6107