Professor of Mathematics
University of Bath

Department of Mathematical Sciences
University of Bath
Bath, BA2 7AY
+44(0)1225 38 6457
4 West 3.37


I am interested in understanding and predicting the behaviour of complicated random events and processes, in particular when there are network or spatial structures involved. Most of my work is connected to the idea of emergence: how large scale order can be created out of the random interactions of individual particles or organisms. The problems I work on come from a wide range of sources, including:

  • Random matrix theory
  • Networks and epidemics
  • Ecology and evolution
  • Stochastic processes


  1. Fitness differences suppress the number of mating types in evolving isogamous species
    Yvonne Krumbeck, George W. A. Constable, Tim Rogers preprint (2019)
  2. Universal hypotrochoidic law for random matrices with cyclic correlations
    Pau Vilimelis Aceituno, Tim Rogers, Henning Schomerus Phys Rev E (2019)
  3. New framework for automated article selection applied to a literature review of Enhanced Biological Phosphorus Removal
    Minh Nguyen Quang, Tim Rogers, Jan Hofman, Ana B. Lanham PLOS One (2019)
  4. Spectral Theory of Sparse Non-Hermitian Random Matrices
    (Topical Review) Izaak Neri, Fernando Metz, Tim Rogers Journal of Physics A: Mathematical and Theoretical (2019)
  5. The invasion speed of cell migration models with realistic cell cycle time distributions
    Enrico Gavagnin, Matthew J. Ford, Richard L. Mort, Tim Rogers, Christian A. Yates Journal of Theoretical Biology (2018)
  6. The Nested Kingman Coalescent: Speed of Coming Down from Infinity
    Airam Blancas Benítez, Tim Rogers, Jason Schweinsberg, Arno Siri-Jégousse Annals of Applied Probability (2018)
  7. The effect of population abundances on the stability of large random ecosystems
    Theo Gibbs, Jacopo Grilli, Tim Rogers, Stefano Allesina Phys Rev E (2018)
  8. Noise-driven bias in the non-local voter model
    Kevin Minors, Tim Rogers, Christian A Yates Europhysics Letters (2018)
  9. A re-entrant phase transition in the survival of secondary infections on networks
    Sam Moore, Peter Mörters and Tim Rogers Journal of Statistical Physics (2017)
  10. Demographic noise slows down cycles of dominance
    Qian Yang, Tim Rogers, and Jonathan Dawes Journal of Theoretical Biology (2017)
  11. Heterogeneous micro-structure of percolation in sparse networks
    Reimer Kühn and Tim Rogers Europhysics Letters (2017)
  12. Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology
    Todd Parsons and Tim Rogers Journal of Physics A (2017) "Highlight of 2017"
  13. A phase transition in excursions from infinity of the "fast" fragmentation-coalescence process
    Andreas Kyprianou, Steven Pagett, Tim Rogers and Jason Schweinsberg Annals of Probability (2017)
  14. Universality in a class of fragmentation-coalescence processes
    Andreas Kyprianou, Steven Pagett, and Tim Rogers AIHP (2017)
  15. Dual-specificity phosphatase 5 controls the localized inhibition, propagation, and transforming potential of ERK signaling
    Andrew M. Kidger, Linda K. Rushworth, Julia Stellzig, Jane Davidson, Christopher J. Bryant, Cassidy Bayley, Edward Caddye, Tim Rogers, Stephen M. Keyse, and Christopher J. Caunt PNAS (2017)
  16. Demographic noise can reverse the direction of deterministic selection
    George Constable, Tim Rogers, Alan McKane and Corina Tarnita PNAS (2016)
  17. Modularity and stability in ecological communities
    Jacopo Grilli, Tim Rogers and Stefano Allesina Nature Communications, 7, 12031 (2016)
  18. Network Inoculation: Heteroclinics and phase transitions in an epidemic model
    Hui Yang, Tim Rogers and Thilo Gross arXiv:1604.02630 Chaos, Volume 26, Issue 8 10.1063/1.4961249
  19. From empirical data to time-inhomogeneous continuous Markov processes
    Pedro Lencastre, Frank Raischel, Tim Rogers, and Pedro G. Lind arXiv:1510.07282 Phys. Rev. E 93, 032135 (2016)
  20. Scale-invariant geometric random graphs
    Zheng Xie and Tim Rogers arXiv:1505.01332 Phys. Rev. E 93, 032310 (2016)
  21. Assessing node risk and vulnerability to epidemics on networks
    Tim Rogers Europhys. Lett. 109, 28005 (2015) "Editor's Choice"
  22. Modes of competition and the fitness of evolved populations
    Tim Rogers, Alan McKane arXiv:1407.3137 Phys. Rev. E 92, 032708 (2015) "Editor's Suggestion"
  23. Growth-induced breaking and unbreaking of ergodicity in fully-connected spin systems
    Richard Morris, Tim Rogers arXiv:1404.7317 J. Phys. A: Math. Theor. 47 342003 (2014)
  24. Current noise-removal methods can create false signals in ecogenomic data
    Axel G Rossberg, Tim Rogers, Alan J McKane Full text Proc. R. Soc. B: Biol. (2014) 281, 1783
  25. Null models for dynamic centrality in temporal networks
    Tim Rogers Journal of Complex Networks (2014)
  26. Stochastic pattern formation and spontaneous polarisation: the linear noise approximation and beyond
    Alan J McKane, Tommaso Biancalani, Tim Rogers arXiv:1211.0462 Bull. Math. Biol. 76, 4, pp 895-921 (2014)
  27. Consensus time and conformity in the adaptive voter model
    Tim Rogers, Thilo Gross arXiv:1304.4742 Phys. Rev. E 88, 030102(R) (2013)
  28. Are there species smaller than 1mm?
    Axel G Rossberg, Tim Rogers, Alan J McKane Open access Proc. R. Soc. B: Biol. (2013) 280, 1767
  29. Stochastic dynamics on slow manifolds
    George W A Constable, Alan J McKane, Tim Rogers arXiv:1301.7697 J. Phys. A: Math. Theor. 46, 295002 (2013)
  30. Voter models with conserved dynamics
    Fabio Caccioli, Luca Dall'Asta, Tobias Galla, Tim Rogers arXiv:1208.2050 Phys. Rev. E. 87, 052114 (2013)
  31. Spontaneous genetic clustering in populations of competing organisms
    Tim Rogers, Alan J McKane, Axel G Rossberg arXiv:1207.1615 Phys. Biol. 9, 066002 (2012)
  32. Stochastic oscillations of adaptive networks:application to epidemic modelling
    Tim Rogers, William Clifford-Brown, Catherine Mills, Tobias Galla arXiv:1206.2768 J. Stat. Mech. P08018 (2012)
  33. Noise-induced metastability in biochemical networks
    Tommaso Biancalani, Tim Rogers, Alan J McKane arXiv:1204.4341 Phys. Rev. E 86, 010106 (Rapid Communications) (2012)
  34. Jamming and pattern formation in models of segregation
    Tim Rogers, Alan J McKane arXiv:1204.5400 Phys. Rev. E 85, 041136 (2012)
  35. Demographic noise can lead to the spontaneous formation of species
    Tim Rogers, Alan J McKane, Axel G Rossberg arXiv:1111.1152 Europhys. Lett. 97, 40008 (2012) "Editor's Choice"
  36. A unified framework for Schelling's model of segregation
    Tim Rogers, Alan J McKane arXiv:1104.1971 J. Stat. Mech. P07006 (2011)
  37. Maximum-entropy moment-closure for stochastic systems on networks
    Tim Rogers arXiv:1103.4980 J. Stat. Mech. P05007 (2011)
  38. Universal sum and product rules for random matrices
    Tim Rogers arXiv:0912.2499 J. Math. Phys. 51, 093304 (2010)
  39. Spectral density of random graphs with topological constraints
    Tim Rogers, Conrad Pérez Vicente, Koujin Takeda, Isaac Pérez Castillo arXiv:0910.3556 J. Phys. A: Math. Theor. 43 195002, (2010)
  40. Cavity approach to the spectral density of non-Hermitian sparse matrices
    Tim Rogers, Isaac Pérez Castillo arXiv:0810.0991 Phys. Rev. E. 79, 012101 (2009)
  41. Cavity approach to the spectral density of sparse symmetric random matrices
    Tim Rogers, Koujin Takeda, Isaac Pérez Castillo, Reimer Kühn
    Phys. Rev. E. 78, 031116 (2008)
spherical law

PhD Thesis:

New Results on the Spectral Density of Random Matrices
King's College London (2010)



Are you interested in using mathematics to study complex real-world phenomena? I have many more research questions than I have time to work on, so I am always looking for enthusiastic people to work with. Opportunities include:
  • Summer research projects
  • Masters dissertations
  • PhD projects
  • Postdoctoral researchers and fellows
  • International visitors
Contact me to find out more.

Current and former PhD students: