Publications of Geoffrey Grimmett

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

- arXiv.org
- Google Scholar
- MathSciNet
- Erdös–Bacon number 5 (= 2 + 3)
- Apportionment of the European Parliament

**Mathematics of Multiscale Materials, Springer 1999**(ed., with K. Golden, R. James, G. Milton, P. Sen). IMA Volumes in Mathematics and its Applications, vol. 99.**Percolation, Second edition, Springer 1999.**Table of contents, preface, and two sample chapters.**Disorder in Physical Systems, 2001**(ed., with Dominic Welsh). The complete electronic version of the Festschrift for John Hammersley, originally published in 1990 by OUP.**Probability and Phase Transition, 2004**. The complete electronic Proceedings of a NATO Advanced Study Institute held at the Isaac Newton Institute, Cambridge, 1993, listed here by gracious permission of Springer.**The Random-Cluster Model, Springer 2006**. Complete text.-
**Combinatorics, Complexity and Chance**, A Tribute to Dominic Welsh (ed., with C. J. H. McDiarmid), Oxford University Press, 2007. -
**Percolation Theory at Saint-Flour, Springer 2012**(with Harry Kesten). **Probability, an Introduction, Second edition, OUP 2014**(with Dominic Welsh).-
**Probability on Graphs, Second edition, Cambridge University Press 2018**. Complete text. **Probability and Random Processes, Fourth edition, OUP 2020**(with David Stirzaker).**One Thousand Exercises in Probability, Third edition, OUP 2020**(with David Stirzaker).

- The work of Hugo Duminil-Copin

INSMI (CNRS) Newsletter 5 July 2022 (French tr., V. Beffara)

arxiv, pdf - Selected problems in probability theory

In*Mathematics Going Forward*

Springer Lecture Notes in Mathematics 2313, 2022, eds J.-M. Morel, B. Teissier

arxiv, pdf -
Percolation critical probabilities of matching lattice-pairs
*with Zhongyang Li*

arxiv, pdf -
Hyperbolic site percolation
*with Zhongyang Li*

arxiv, pdf -
Brownian snails with removal: epidemics in diffusing populations
*with Zhongyang Li*

Electronic Journal of Probability 27 (2022) article 78, 31 pp.

arxiv, pdf, EJP -
Tom Liggett, some brief reflections

Celebratio Mathematica, Thomas Milton Liggett (2021)

pdf -
Harry Kesten's work in probability theory

Probability Theory and Related Fields 181 (2021) 17–56

arxiv, pdf

Published version: Editorial, HK publication list, Article text -
Harry Kesten (1931–2019), a personal and scientific tribute
*with Greg Lawler*

Notices of the AMS 67 (2020), 822–831

arxiv, published pdf, pdf (1mb) -
The lost boarding pass, and other practical problems
*with David Stirzaker*

The Mathematical Gazette 105 (2021) 216–221

arxiv, pdf -
Alignment percolation
*with Nicholas Beaton and Mark Holmes*

Mathematical Physics, Analysis and Geometry 24 (2021) article 3

arxiv, pdf -
Non-coupling from the past
*with Mark Holmes*

In*In and Out of Equilibrium 3. Celebrating Vladas Sidoravicius*

Springer, 2021, 471–485

arxiv, pdf -
Bounded entanglement entropy in the quantum Ising model
*with Tobias Osborne and Petra Scudo*

Journal of Statistical Physics 178 (2020) 281–296

arxiv, published pdf -
Weighted self-avoiding walks
*with Zhongyang Li*

Journal of Algebraic Combinatorics 52 (2020) 77--102

arxiv, published pdf -
On influence and compromise in two-tier voting systems

Mathematical Social Sciences 100 (2019) 35–45

arxiv, pdf -
A 700-seat no-loss composition for the 2019 European Parliament
*with F. Pukelsheim, V. Ramírez González, W. Słomczyński, K. Życzkowski*

arxiv, pdf -
Degressive representation of Member States in the European Parliament
2019–2024
*with Friedrich Pukelsheim*

Representation 54 (2018) 147–158

arxiv, pdf -
Self-avoiding walks and connective constants
*with Zhongyang Li*

In*Sojourns in Probability Theory and Statistical Physics, III*

Springer Proceedings in Mathematics & Statistics, vol. 300, 2019, pages 215–241, ed. V. Sidoravicius

arxiv, pdf -
The composition of the European Parliament
*with Friedrich Pukelsheim*

In*The Composition of the European Parliament*

Policy Department for Citizens' Rights and Constitutional Affairs PE 583.117, February 2017

pdf, published version -
Cubic graphs and the golden mean
*with Zhongyang Li*

Discrete Mathematics 343 (2020) paper 111638

arxiv, published pdf -
Self-avoiding walks and amenability
*with Zhongyang Li*

The Electronic Journal of Combinatorics 24 (2017) paper P4.38, 24 pp

arxiv, pdf -
The 1-2 model
*with Zhongyang Li*

*In the Tradition of Ahlfors–Bers, VII*

Proceedings of the Sixth Ahlfors–Bers Colloquium, 2014

Contemporary Mathematics 696 (2017) 130–152

arxiv, pdf -
Critical surface of the 1-2 model
*with Zhongyang Li*

International Mathematics Research Notices 21 (2018) 6617–6672

arxiv, pdf -
Connective constants and height functions of Cayley graphs
*with Zhongyang Li*

Transactions of the American Mathematical Society 369 (2017) 5961–5980

arxiv, pdf -
Counting self-avoiding walks
*with Zhongyang Li*

Accepted in*Tsinghua Lectures in Mathematics*, 2017

arxiv, pdf -
Locality of connective constants
*with Zhongyang Li*

Discrete Mathematics 341 (2018) 3483–3497

arxiv, pdf -
The Potts and random-cluster models

arxiv, pdf -
The work of Lucio Russo on percolation

Mathematics and Mechanics of Complex Systems 4 (2016) 199–211

arxiv, pdf -
Correlation inequalities for the Potts model

Mathematics and Mechanics of Complex Systems 4 (2016) 327–334

arxiv, pdf -
Critical surface of the hexagonal polygon model
*with Zhongyang Li*

Journal of Statistical Physics 163 (2016) 733–753

arxiv, pdf -
Influence in product spaces
*with Svante Janson and James Norris*

in*Probability, Analysis and Number Theory*

Advances in Applied Probability 48A (2016) 145–152

arxiv, pdf -
Bounds on connective constants of regular graphs
*with Zhongyang Li*

Combinatorica 35 (2015) 279–294

arxiv, pdf -
Criticality, universality, and isoradiality

Proceedings of 2014 International Congress of Mathematicians, Seoul, vol IV, 25–48

arxiv, pdf -
Extendable self-avoiding walks
*with Alexander Holroyd and Yuval Peres*

Annales de l'Institut Henri Poincaré D: CPI 1 (2014) 61–75

arxiv, pdf -
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 -
Strict inequalities for connective constants of transitive graphs
*with Zhongyang Li*

SIAM Journal of Discrete Mathematics 28 (2014) 1306–1333

arxiv, pdf -
Bond percolation on isoradial graphs: criticality and universality
*with Ioan Manolescu*

Probability Theory and Related Fields 159 (2014) 273–327

arxiv, pdf -
Self-avoiding walks and the Fisher transformation
*with Zhongyang Li*

The Electronic Journal of Combinatorics 20 (2013), Paper P3.47, 14 pp

arxiv, pdf -
Universality for bond percolation in two dimensions
*with Ioan Manolescu*

Annals of Probability 41 (2013) 3261–3283

arxiv, pdf -
Inhomogeneous bond percolation on square, triangular, and hexagonal lattices
*with Ioan Manolescu*

Annals of Probability 41 (2013) 2990–3025

arxiv, pdf -
Cluster detection in networks using percolation
*with Ery Arias-Castro*

Bernoulli 19 (2013) 676–719

arxiv, pdf -
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 -
Stochastic geometry and statistical mechanics

Markov Processes and Related Fields 18 (2012) 67–70

pdf -
Geometry of Lipschitz percolation
*with Alexander Holroyd*

Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 48 (2012) 309–326

arxiv, pdf -
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 -
European apportionment via the Cambridge Compromise

Mathematical Social Sciences 63 (2012) 68–73

arxiv, pdf -
Lattice embeddings in percolation
*with Alexander Holroyd*

Annals of Probability 40 (2012) 146–161

arxiv, pdf -
Three theorems in discrete random geometry

Probability Surveys 8 (2011) 403–441

arxiv, pdf, erratum to PrS version -
The allocation between the EU Member States of the seats in the European Parliament

European Parliament Studies, PE 432.760, March 2011

pdf -
Sharp thresholds for the random-cluster and Ising models
*with Benjamin Graham*

Annals of Applied Probability 21 (2011) 240–265

arxiv, pdf -
Plaquettes, spheres, and entanglement
*with Alexander Holroyd*

Electronic Journal of Probability 15 (2010) 1415–1428

arxiv, pdf -
Lipschitz percolation
*with Nicolas Dirr, Patrick Dondl, Alexander Holroyd, Michael Scheutzow*

Electronic Communications in Probability 15 (2010) 14–21

arxiv, pdf -
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 -
Random graphs with forbidden vertex degrees
*with Svante Janson*

Random Structures and Algorithms 37 (2010) 137–175

arxiv, pdf -
Percolation of arbitrary words in one dimension
*with Thomas Liggett and Thomas Richthammer*

Random Structures and Algorithms 37 (2010) 85–99

arxiv, pdf -
The phase transition of the quantum Ising model is sharp
*with Jakob Björnberg*

Journal of Statistical Physics 136 (2009) 231–273

arxiv, pdf -
David George Kendall (1918–2007)

Journal of the Royal Statistical Society, Series A 172 (2009) 275–278

arxiv, pdf -
Random even graphs
*with Svante Janson*

The Electronic Journal of Combinatorics 16 (2009), Paper R46, 19 pp

arxiv, pdf -
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 -
Entanglement in the quantum Ising model
*with Tobias Osborne and Petra Scudo*

Journal of Statistical Physics 131 (2008) 305–339

arxiv, pdf -
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 -
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 -
Random-cluster representation of the Blume–Capel model
*with Benjamin Graham*

Journal of Statistical Physics 25 (2006) 283–316

arxiv, pdf, remarks -
Influence and sharp-threshold theorems for monotonic measures
*with Benjamin Graham*

Annals of Probability 34 (2006) 1726–1745

arxiv, pdf -
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 -
Branching processes, and random-cluster measures on trees
*with Svante Janson*

Journal of the European Mathematical Society 7 (2005) 253–281

arxiv, pdf -
John Michael Hammersley, 1920–2004

The Independent, 14 May 2004

html with photo, pdf -
Weak limits of quantum random walks
*with Svante Janson and Petra Scudo*

Physical Review E 69 (2004) Paper 026119

arxiv, pdf -
Negative association in uniform forests and connected graphs
*with Stephan Winkler*

Random Structures and Algorithms 24 (2004) 444–460

arxiv, pdf - Stochastic apportionment

American Mathematical Monthly 111 (2004) 299–307

arxiv, pdf - On smallest triangles
*with Svante Janson*

Random Structures and Algorithms 23 (2003) 206–223

arxiv, pdf - The random-cluster model

in*Probability on Discrete Structures*,

ed. H. Kesten, Encyclopedia of Mathematical Sciences, vol. 110, Springer, 2003, 73–123

arxiv, pdf - Rigidity of the interface in percolation and random-cluster models
*with Guy Gielis*

Journal of Statistical Physics 109 (2002) 1–37

arxiv, pdf - Directed percolation and random walk
*with Philipp Hiemer*

in*In and Out of Equilibrium*, ed. V. Sidoravicius, Birkhäuser, 2002, 273–297

arxiv, pdf - Random electrical networks on complete graphs II: Proofs
*with Harry Kesten*

1983, 51 pages

arxiv, July 2001; pdf - Diffusion,
finance, and universality

Asymptopia, June 2001

html - Infinite paths in randomly oriented lattices

Random Structures and Algorithms 18 (2001) 257–266

pdf - 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 - Entanglement in percolation
*with Alexander Holroyd*

Proceedings of the London Mathematical Society 81 (2000) 485–512

pdf - Percolation

in*Development of Mathematics 1950–2000*,

ed. J.-P. Pier, Birkhäuser, 2000, 547-576

pdf - Stochastic pin-ball

in*Random Walks and Discrete Potential Theory*,

ed. M. Picardello and W. Woess, Cambridge University Press, 1999, 205–213

pdf - 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 - 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 - Critical probabilities
for site and bond percolation models
*with Alan Stacey*

Annals of Probability 26 (1998) 1788–1812

pdf - What a coincidence!

+pass issue 4, January 1998

html - Percolation
and minimal spanning trees
*with Carol Bezuidenhout and Armin Löffler*

Journal of Statistical Physics 92 (1998) 1–34

pdf - Dependent random graphs
and spatial epidemics
*with Rob van den Berg and Rinaldo Schinazi*

Annals of Applied Probability 8 (1998) 317–336

pdf - 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 - Decay of correlations in subcritical
Potts and random-cluster models,
*with Marcelo Piza*

Communications in Mathematical Physics 189 (1997) 465–480

pdf - Large deviations
in the random sieve,

Mathematical Proceedings of the Cambridge Philosophical Society 121 (1997) 519–530

pdf - Random walks
in random labyrinths
*with Misha Menshikov and Stas Volkov*

Markov Processes and Related Fields 2 (1996) 69–86

pdf - The random-cluster model on the complete graph
*with Béla Bollobás and Svante Janson*

Probability Theory and Related Fields 104 (1996) 283–317

pdf - Comparison and disjoint-occurrence inequalities for random-cluster models

Journal of Statistical Physics 78 (1995) 1311–1324

pdf - The stochastic random-cluster process and the uniqueness
of random-cluster measures

Annals of Probability 23 (1995) 1461–1510

pdf - The random-cluster model

in*Probability, Statistics and Optimization: A Tribute to Peter Whittle*

ed. F. P. Kelly, 1994, 49–63, Wiley

pdf - Potts models and random-cluster models with many-body interactions

Journal of Statistical Physics 75 (1994) 67–121

pdf - Percolative problems

in*Probability and Phase Transition*,

ed. Geoffrey Grimmett, 1994, 69–86, Kluwer

pdf - Differential inequalities for Potts and random-cluster processes

in*Cellular Automata and Cooperative Systems*,

ed. N. Boccara et al., 1993, 227–236, Kluwer

pdf - 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 - 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

Introspective Classification for Robot
Perception and Decision Making

DPhil Thesis, University of Oxford, 2016

pdf