Publications and Preprints
Please see below for a list of publications and preprints from the current members of the Probability Group. Some articles may have accompanying data sets, simulations or code. This information can be found through the relevant author's website, these can be accessed here.
2021 - 2025
Freeman, N. and Swart, J.M., 2023. Weaves, webs and flows. (arXiv)
Freeman, N. and Swart, J.M., 2022. Skorohod's topologies on path space. (arXiv)
Haslegrave, J., Jordan, J. and Yarrow, M., 2022. Competing types in preferential attachment graphs with community structure. (arXiv)
Jordan, J. and Costa, M., 2022. Phase transitions in non-linear urns with interacting types. Bernoulli 28(4), pp.2546-2562. (Journal and arXiv)
Andrews, B. and Jordan, J., 2021. Rarity of non-convergence in preferential attachment graphs with three types. Involve 14(3), pp.531-540. (Journal and arXiv)
Grauer, A., Lüchtrath, L. and Yarrow, M., 2021. Preferential attachment with location-based choice: Degree distribution in the noncondensation phase. Journal of Statistical Physics, 184(1), pp.1-16. (Journal and arXiv)
2016 - 2020
Applebaum, D. and Shewell Brockway, R., 2020. L^2 Properties of Lévy Generators on Compact Riemannian Manifolds. Journal of Theoretical Probability, pp.1-14.. (Journal and arXiv)
Brimkov, B., Duna, K., Hogben, L., Lorenzen, K., Reinhart, C., Song, S.Y. and Yarrow, M., 2020. Graphs that are cospectral for the distance Laplacian. The Electronic Journal of Linear Algebra, 36(36), pp.334-351. (Journal and arXiv)
Freeman, N. and Jordan, J., 2020. Extensive condensation in a model of preferential attachment with fitness. Electronic Journal of Probability, 25. (Journal and arXiv)
Freeman, N. and Palau, S., 2020. A Note on Characterizing Tightness of Random Sets of Cadlag Paths. Lecture Notes Series-Institute for Mathematical Sciences National University of Singapore: Genealogies of Interacting Particle Systems, 38, pp.295-313. (Journal and Website)
Haslegrave, J., Jordan, J. and Yarrow, M., 2020. Condensation in preferential attachment models with location‐based choice. Random Structures & Algorithms, 56(3), pp.775-795. (Journal and arXiv)
Goldschmidt, C. and Stephenson, R., 2019. The scaling limit of a critical random directed graph. (Preprint, arXiv)
Haas, B. and Stephenson, R., 2019. Scaling limits of multi-type Markov Branching trees. (Preprint, arXiv)
Haas, B. and Stephenson, R., 2018. Bivariate Markov chains converging to Lamperti transform Markov additive processes. Stochastic Processes and their Applications, 128(10), pp.3558-3605. (Journal and arXiv)
Haslegrave, J. and Jordan, J., 2018. Non-convergence of proportions of types in a preferential attachment graph with three co-existing types. Electronic Communications in Probability, 23. (Journal and arXiv)
Jordan, J. 2018. Preferential attachment graphs with co-existing types of different fitnesses. Journal of Applied Probability, 55(4), pp.1211-1227. (Journal and arXiv)
Jordan, J., 2018. The connected component of the partial duplication graph. ALEA, 15, pp.1431-1445. (Journal and arXiv)
Stephenson, R. 2018. Local convergence of large critical multi-type Galton–Watson trees and applications to random maps. Journal of Theoretical Probability, 31(1), pp.159-205.(Journal and arXiv)
Stephenson, R., 2018. On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees. ALEA, 15, pp.1257-1292. (Journal and arXiv)
Etheridge, A., Freeman, N. and Penington, S., 2017. Branching Brownian motion, mean curvature flow and the motion of hybrid zones. Electronic Journal of Probability, 22. (Journal and arXiv)
Etheridge, A., Freeman, N., Penington, S. and Straulino, D., 2017. Branching Brownian motion and selection in the spatial $\Lambda $-Fleming–Viot process. Annals of Applied Probability, 27(5), pp.2605-2645. (Journal and arXiv)
Etheridge, A., Freeman, N. and Straulino, D., 2017. The Brownian net and selection in the spatial $\Lambda $-Fleming-Viot process. Electronic Journal of Probability, 22. (Journal and arXiv)
Bertoin, J. and Stephenson, R., 2016. Local explosion in self-similar growth-fragmentation processes. Electronic Communications in Probability, 21. (Journal and arXiv)
Haslegrave, J. and Jordan, J., 2016. Preferential attachment with choice. Random Structures & Algorithms, 48(4), pp.751-766. (Journal and arXiv)
2011 - 2015
Crane, E., Freeman, N. and Tóth, B., 2015. Cluster growth in the dynamical Erdős-Rényi process with forest fires. Electronic Journal of Probability, 20. (Journal and arXiv)
Freeman, N., 2015. The segregated $\Lambda $-coalescent. Annals of Probability, 43(2), pp.435-467. (Journal and arXiv)
Haas, B. and Stephenson, R., 2015. Scaling limits of $ k $-ary growing trees. In Annales de l'IHP Probabilités et statistiques (Vol. 51, No. 4, pp. 1314-1341). (Journal and arXiv)
Jordan, J. and Wade, A.R., 2015. Phase transitions for random geometric preferential attachment graphs. Advances in Applied Probability, 47(2), pp.565-588. (Journal and arXiv)
Cannings, C. and Jordan, J., 2013. Random walk attachment graphs. Electronic Communications in Probability, 18. (Journal and arXiv)
Irons, D.J. and Jordan, J., 2013. Geometric networks based on Markov point processes with applications to mobile sensor networks. In 2013 2nd International Conference on Mechanical Engineering, Industrial Electronics and Informatization (MEIEI 2013) (pp. 1-17). (Preprint)
Jordan, J., 2013. Geometric preferential attachment in non-uniform metric spaces. Electronic Journal of Probability, 18. (Journal and arXiv)
Stephenson, R., 2013. General fragmentation trees. Electronic Journal of Probability, 18. (Journal and arXiv)
Jordan, J., 2011. Randomised reproducing graphs. Electronic Journal of Probability, 16, pp.1549-1562. (Journal and arXiv)
2006 - 2010
Cohen, N., Jordan, J. and Voliotis, M., 2010. Preferential duplication graphs. Journal of Applied Probability, 47(2), pp.572-585. (Journal and ResearchGate)
Jordan, J., 2010. Degree sequences of geometric preferential attachment graphs. Advances in Applied Probability, 42(2), pp.319-330. (Journal and ResearchGate)
Jordan, J., 2010. The spectra of the Laplacians of fractal graphs not satisfying spectral decimation. Proceedings of the Edinburgh Mathematical Society, 53(3), pp.731-746. (Journal and ResearchGate)
Jordan, J. and Southwell, R., 2010. Further properties of reproducing graphs. Applied Mathematics, 1(05), p.344. (Journal and ResearchGate)
Jordan, J., 2009. Comb graphs and spectral decimation. Glasgow Mathematical Journal, 51(1), pp.71-81. (Journal and White Rose)
Blackwell, P., Edmondson-Jones, M. and Jordan, J., 2007. Spectra of adjacency matrices of random geometric graphs. University of Sheffield. Department of Probability and Statistics. (Preprint)
2001 - 2005
Jordan, J., 2006. Spectrum of the Laplacian of an asymmetric fractal graph. Proceedings of the Edinburgh Mathematical Society, 49(1), pp.101-113. (Journal and ResearchGate)
Jordan, J., 2006. The degree sequences and spectra of scale‐free random graphs. Random Structures & Algorithms, 29(2), pp.226-242. (Journal and Personal Website)
Hambly, B.M. and Jordan, J., 2004. A random hierarchical lattice: the series-parallel graph and its properties. Advances in applied probability, pp.824-838. (Journal and JStor)
Jordan, C.R., Jordan, D.A. and Jordan, J.H., 2002. Reversible complex Hénon maps. Experimental mathematics, 11(3), pp.339-347. (Journal and Project Euclid)
Jordan, J., 2002. Almost sure convergence for iterated functions of independent random variables. Annals of Applied Probability, pp.985-1000. (Journal and Project Euclid)