Pre-prints and Publications

Competing types in preferential attachment graphs with community structure (2022)

(With John Haslegrave and Mark Yarrow)

Preprint

Phase transitions in non-linear urns with interacting types (2022)
(With Marcelo Costa)
Bernoulli, vol. 28, no. 4, pp2546-2562

Fragility of non-convergence in preferential attachment graphs with three types (2021)
(With Ben Andrews)
Involve, vol. 14, no. 3, pp531-540.

Extensive Condensation in a model of Preferential Attachment with Fitnesses (2020)
(With Nic Freeman)
Electronic Journal of Probability, vol. 25, paper no. 68, pp.1-42.

Condensation in preferential attachment models with location-based choice (2020)
(With John Haslegrave and Mark Yarrow)
Random Structures and Algorithms, vol. 56, issue 3, pp. 775-795.

Non-convergence of proportions of types in a preferential attachment graph with three co-existing types (2018)
(With John Haslegrave)
Electronic Communications in Probability, vol. 23, no. 54, pp. 1-12.

Preferential attachment graphs with co-existing types of different fitnesses (2018)
Journal of Applied Probability, vol. 55, no. 4, pp. 1211-1227.

The connected component of the partial duplication graph (2018)
ALEA, vol. 15, pp. 1431-1445

Preferential attachment with choice (2016)
(With John Haslegrave)
Random Structures and Algorithms, vol. 48, no. 4, pp. 751-766

Phase transitions for random geometric preferential attachment graphs (2015)
(With Andrew Wade)
Advances in Applied Probability, vol. 47, no. 2, pp. 565-588.

Random walk attachment graphs (2013)
(With Chris Cannings)
Electronic Communications in Probability, vol. 18, no. 77, pp. 1-5.

Geometric preferential attachment in non-uniform metric spaces (2013)
Electronic Journal of Probability, vol. 18, no. 8, pp. 1-15.

Randomised reproducing graphs (2011)
Electronic Journal of Probability, vol. 16, pp. 1549-1562.

Geometric networks based on Markov point processes with applications to mobile sensor networks
(With David Irons)
Preprint.

Further properties of reproducing graphs (2010)
(With Richard Southwell)
Applied Mathematics, vo1. 1, no. 5, pp. 344-350.

Preferential duplication graphs (2010)
(With Netta Cohen and Margaritis Voliotis)
Journal of Applied Probability, vol. 47, no. 2, pp. 572-585.

Degree sequences of geometric preferential attachment graphs (2010)
Advances in Applied Probability, vol. 42, no. 2, pp. 319-330.

The spectra of the Laplacians of fractal graphs not satisfying spectral decimation (2010)
Proceedings of the Edinburgh Mathematical Society, vol. 53, pp. 731-746.

Comb graphs and spectral decimation (2009)
Glasgow Mathematical Journal, vol. 51, pp. 71-81.

Spectra of adjacency matrices of random geometric graphs
(With Paul Blackwell and Mark Edmondson Jones)
Preprint.

The degree sequences and spectra of scale-free random graphs (2006)
Random Structures and Algorithms, vol. 29, no. 2, pp. 226-242.

Spectrum of the Laplacian of an asymmetric fractal graph (2006)
Proceedings of the Edinburgh Mathematical Society, vol. 49, no. 1, pp. 101-113.

A random hierarchical lattice: the series-parallel graph and its properties (2004)
(With Ben Hambly)
Advances in Applied Probability, vol. 36, no. 3, pp. 824-838.

Almost sure convergence for iterated functions of independent random variables (2002)
The Annals of Applied Probability, Vol.12, No.3, pp. 985-1000

Reversible Complex Hénon Maps (2002)
(With Camilla Jordan and David Jordan)
Experimental Mathematics, Vol.11, No.3, pp. 339-347