Publications of Geoffrey Grimmett

The copyright of all linked material resides with the authors, unless it has been assigned to a journal or publisher.

Books

Articles since around 1993

  1. Locality of connective constants, I. Transitive graphs
    with Zhongyang Li
    arxiv, pdf
  2. The Potts and random-cluster models
    arxiv, pdf
  3. Criticality, universality, and isoradiality
    Proceedings of 2014 ICM, Seoul
    arxiv, pdf
  4. Extendable self-avoiding walks
    with Alexander Holroyd and Yuval Peres
    Annales de l'Institut Henri Poincaré D: CPI 1 (2014) 61–75
    arxiv, pdf
  5. Counting self-avoiding walks
    with Zhongyang Li
    arxiv, pdf
  6. Percolation of finite clusters and infinite surfaces
    with Alexander Holroyd and Gady Kozma
    Mathematical Proceedings of the Cambridge Philosophical Society 156 (2014) 263–279
    arxiv, pdf
  7. Strict inequalities for connective constants of transitive graphs
    with Zhongyang Li
    SIAM Journal of Discrete Mathematics 28 (2014) 1306–1333
    arxiv, pdf
  8. Bounds on connective constants of regular graphs
    with Zhongyang Li
    Combinatorica
    arxiv, pdf
  9. Self-avoiding walks and the Fisher transformation
    with Zhongyang Li
    Electronic Journal of Combinatorics 20 (2013), Paper P47, 14 pp
    arxiv, pdf
  10. Influences in product spaces: BKKKL re-revisited
    with Svante Janson and James Norris
    arxiv, pdf
  11. Bond percolation on isoradial graphs: criticality and universality
    with Ioan Manolescu
    Probability and Related Fields 159 (2014) 273–327
    arxiv, pdf
  12. Universality for bond percolation in two dimensions
    with Ioan Manolescu
    Annals of Probability 41 (2013) 3261–3283
    arxiv, pdf
  13. Inhomogeneous bond percolation on square, triangular, and hexagonal lattices
    with Ioan Manolescu
    Annals of Probability 41 (2013) 2990–3025
    arxiv, pdf
  14. Cluster detection in networks using percolation
    with Ery Arias-Castro
    Bernoulli 19 (2013) 676–719
    arxiv, pdf
  15. Percolation since Saint-Flour
    with Harry Kesten
    In Percolation Theory at Saint-Flour
    by Geoffrey Grimmett and Harry Kesten, Springer, 2012, ix–xxvii
    arxiv, pdf
  16. Stochastic geometry and statistical mechanics
    Markov Processes and Related Fields 18 (2012) 67–70
    pdf
  17. Geometry of Lipschitz percolation
    with Alexander Holroyd
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 48 (2012) 309–326
    arxiv, pdf
  18. A power-weighted variant of the EU27 Cambridge Compromise
    with Kai-Friederike Oelbermann and Friedrich Pukelsheim
    Mathematical Social Sciences 63 (2012) 136–140
    arxiv, pdf
  19. European apportionment via the Cambridge Compromise
    Mathematical Social Sciences 63 (2012) 68–73
    arxiv, pdf
  20. Lattice embeddings in percolation
    with Alexander Holroyd
    Annals of Probability 40 (2012) 146–161
    arxiv, pdf
  21. Three theorems in discrete random geometry
    Probability Surveys 8 (2011) 403–441
    arxiv, pdf, erratum to PrS version
  22. The allocation between the EU Member States of the seats in the European Parliament
    European Parliament Studies, PE 432.760, March 2011
    pdf
  23. Sharp thresholds for the random-cluster and Ising models
    with Benjamin Graham
    Annals of Applied Probability 21 (2011) 240–265
    arxiv, pdf
  24. Plaquettes, spheres, and entanglement
    with Alexander Holroyd
    Electronic Journal of Probability 15 (2010) 1415–1428
    arxiv, pdf
  25. Lipschitz percolation
    with Nicolas Dirr, Patrick Dondl, Alexander Holroyd, Michael Scheutzow
    Electronic Communications in Probability 15 (2010) 14–21
    arxiv, pdf
  26. Three problems for the clairvoyant demon
    in Probability and Mathematical Genetics, Papers in honour of Sir John Kingman
    eds: N. H. Bingham and C. M. Goldie, Cambridge University Press, 2010, 379–396
    arxiv, pdf
  27. Random graphs with forbidden vertex degrees
    with Svante Janson
    Random Structures and Algorithms 37 (2010) 137–175
    arxiv, pdf
  28. Percolation of arbitrary words in one dimension
    with Thomas Liggett and Thomas Richthammer
    Random Structures and Algorithms 37 (2010) 85–99
    arxiv, pdf
  29. The phase transition of the quantum Ising model is sharp
    with Jakob Björnberg
    Journal of Statistical Physics 136 (2009) 231–273
    arxiv, pdf
  30. David George Kendall (1918–2007)
    Journal of the Royal Statistical Society, Series A 172 (2009) 275–278
    arxiv, pdf
  31. Random even graphs
    with Svante Janson
    Electronic Journal of Combinatorics 16 (2009), Paper R46, 19 pp
    arxiv, pdf
  32. Correlation inequalities of GKS type for the Potts model
    First posted 30 July 2007 (v1), revised 7 January 2009
    arxiv, pdf
  33. Space–time percolation
    in In and Out of Equilibrium 2
    eds: V. Sidoravicius, M. E. Vares, vol. 60 of `Progress in Probability' series, Birkhäuser, Boston, 2008, 305–320
    arxiv, pdf
  34. Entanglement in the quantum Ising model
    with Tobias Osborne and Petra Scudo
    Journal of Statistical Physics 131 (2008) 305–339
    arxiv, pdf
  35. John Michael Hammersley (1920–2004)
    with Dominic Welsh
    Biographical Memoirs of Fellows of the Royal Society 53 (2007) 163–183
    Bulletin of the London Mathematical Society 41 (2009) 1125–1143
    arxiv, pdf (updated and recommended)
    Draft entry for the Oxford Dictionary of National Biography
  36. Flows and ferromagnets
    in Combinatorics, Complexity and Chance, A Tribute to Dominic Welsh,
    eds: G. R. Grimmett and C. J. H. McDiarmid, Oxford University Press, 2007, 130–143
    arxiv, pdf, typo
  37. Random-cluster representation of the Blume–Capel model
    with Benjamin Graham
    Journal of Statistical Physics 25 (2006) 283–316
    arxiv, pdf, remarks
  38. Influence and sharp-threshold theorems for monotonic measures
    with Benjamin Graham
    Annals of Probability 34 (2006) 1726–1745
    arxiv, pdf
  39. Uniqueness and multiplicity of infinite clusters
    in Dynamics and Stochastics, Festschrift in Honor of Michael Keane
    ed. D. Denteneer, F. den Hollander, E. Verbitskiy, IMS Lecture Notes – Monograph Series volume 48, 2006, 24–36
    arxiv, pdf
  40. Branching processes, and random-cluster measures on trees
    with Svante Janson
    Journal of the European Mathematical Society 7 (2005) 253–281
    arxiv, pdf
  41. John Michael Hammersley, 1920–2004
    The Independent, 14 May 2004
    html with photo, pdf
  42. Weak limits of quantum random walks
    with Svante Janson and Petra Scudo
    Physical Review E 69 (2004) Paper 026119
    arxiv, pdf
  43. Negative association in uniform forests and connected graphs
    with Stephan Winkler
    Random Structures and Algorithms 24 (2004) 444–460
    arxiv, pdf
  44. Stochastic apportionment
    American Mathematical Monthly 111 (2004) 299–307
    arxiv, pdf
  45. On smallest triangles
    with Svante Janson
    Random Structures and Algorithms 23 (2003) 206–223
    arxiv, pdf
  46. The random-cluster model
    in Probability on Discrete Structures,
    ed. H. Kesten, Encyclopedia of Mathematical Sciences, vol. 110, Springer, 2003, 73–123
    arxiv, pdf
  47. Rigidity of the interface in percolation and random-cluster models
    with Guy Gielis
    Journal of Statistical Physics 109 (2002) 1–37
    arxiv, pdf
  48. Directed percolation and random walk
    with Philipp Hiemer
    in In and Out of Equilibrium, ed. V. Sidoravicius, Birkhäuser, 2002, 273–297
    arxiv, pdf
  49. Random electrical networks on complete graphs II: Proofs
    with Harry Kesten
    1983, 51 pages
    arxiv, July 2001; pdf
  50. Diffusion, finance, and universality
    Asymptopia, June 2001
    html
  51. Infinite paths in randomly oriented lattices
    Random Structures and Algorithms 18 (2001) 257–266
    pdf
  52. Conformal invariance, droplets, and entanglement
    in State of the Art in Probability and Statistics, Festschrift for Willem R. van Zwet,
    ed. M. de Gunst, C. Klaassen, A. van der Vaart, Institute of Mathematical Statistics, Lecture Notes volume 36, 2001, 310–323
    pdf
  53. Entanglement in percolation
    with Alexander Holroyd
    Proceedings of the London Mathematical Society 81 (2000) 485–512
    pdf
  54. Percolation
    in Development of Mathematics 1950–2000,
    ed. J.-P. Pier, Birkhäuser, 2000, 547-576
    pdf
  55. Stochastic pin-ball
    in Random Walks and Discrete Potential Theory,
    ed. M. Picardello and W. Woess, Cambridge University Press, 1999, 205–213
    pdf
  56. A central limit theorem for random walks in random labyrinths
    with Carol Bezuidenhout
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 35 (1999) 631–683
    pdf
  57. Inequalities and entanglements for percolation and random-cluster models,
    in Perplexing Problems in Probability, Festschrift in Honor of Harry Kesten,
    ed. M. Bramson and R. Durrett, 1999, 91–106, Birkhäuser
    pdf
  58. Critical probabilities for site and bond percolation models
    with Alan Stacey
    Annals of Probability 26 (1998) 1788–1812
    pdf
  59. What a coincidence!
    +pass issue 4, January 1998
    html
  60. Percolation and minimal spanning trees
    with Carol Bezuidenhout and Armin Löffler
    Journal of Statistical Physics 92 (1998) 1–34
    pdf
  61. Dependent random graphs and spatial epidemics
    with Rob van den Berg and Rinaldo Schinazi
    Annals of Applied Probability 8 (1998) 317–336
    pdf
  62. Percolation and disordered systems,
    in Lectures in Probability Theory and Statistics, Ecole d'Ete de Probabilites de Saint–Flour XXVI-1996,
    Springer Lecture Notes in Maths no. 1665, ed. P. Bernard, published 1997, pages 153–300
    pdf
    Here is a link to errata. If you have trouble printing pages 86–87, or want a version which prints two pages on one side, you might prefer to download this version
    pdf
    2012 corrected reprint
  63. Decay of correlations in subcritical Potts and random-cluster models,
    with Marcelo Piza
    Communications in Mathematical Physics 189 (1997) 465–480
    pdf
  64. Large deviations in the random sieve,
    Mathematical Proceedings of the Cambridge Philosophical Society 121 (1997) 519–530
    pdf
  65. Random walks in random labyrinths
    with Misha Menshikov and Stas Volkov
    Markov Processes and Related Fields 2 (1996) 69–86
    pdf
  66. The random-cluster model on the complete graph
    with Béla Bollobás and Svante Janson
    Probability Theory and Related Fields 104 (1996) 283–317
    pdf
  67. Comparison and disjoint-occurrence inequalities for random-cluster models
    Journal of Statistical Physics 78 (1995) 1311–1324
    pdf
  68. The stochastic random-cluster process and the uniqueness of random-cluster measures
    Annals of Probability 23 (1995) 1461–1510
    pdf
  69. The random-cluster model
    in Probability, Statistics and Optimization: A Tribute to Peter Whittle
    ed. F. P. Kelly, 1994, 49–63, Wiley
    pdf
  70. Potts models and random-cluster models with many-body interactions
    Journal of Statistical Physics 75 (1994) 67–121
    pdf
  71. Percolative problems
    in Probability and Phase Transition,
    ed. Geoffrey Grimmett, 1994, 69–86, Kluwer
    pdf
  72. Differential inequalities for Potts and random-cluster processes
    in Cellular Automata and Cooperative Systems,
    ed. N. Boccara et al., 1993, 227–236, Kluwer
    pdf
  73. Strict inequality for critical values of Potts models and random-cluster processes
    with Carol Bezuidenhout and Harry Kesten
    Communications in Mathematical Physics 158 (1993) 1–16
    pdf
  74. Percolation in ∞ + 1 dimensions
    with Chuck Newman
    in Disorder in Physical Systems, (festschrift for John Hammersley),
    ed. Geoffrey Grimmett and Dominic Welsh, 1990/2001, 167–190, Oxford University Press
    pdf