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.
Hyperbolic site percolation
with Zhongyang Li Random Structures and Algorithms 66 (2025) paper 21262
arxiv,
pdf, printed version
Non-self-touching paths in plane graphs
Annales de l'Institut Henri Poincaré D (2025)
arxiv,
pdf
2025
Percolation critical probabilities of matching lattice-pairs
with Zhongyang Li Random Structures and Algorithms 65 (2024) 832–856
arxiv,
pdf
Selected problems in probability theory
In Mathematics Going Forward Springer Lecture Notes in Mathematics 2313, 2023, eds J.-M. Morel, B. Teissier, pp. 603–614
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
The Potts and random-cluster models
in Handbook of the Tutte Polynomial and Related Topics CRC Press, ed. J. A. Ellis-Monaghan, I. Moffatt, 2022, 378–394
arxiv,
pdf
Tom Liggett, some brief reflections
Celebratio Mathematica, Thomas Milton Liggett (2021)
pdf
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
Cubic graphs and the golden mean
with Zhongyang Li Discrete Mathematics 343 (2020) paper 111638
arxiv,
published pdf
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)
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
2020
On influence and compromise in two-tier voting systems
Mathematical Social Sciences 100 (2019) 35–45
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
Degressive representation of Member States in the European Parliament
2019–2024
with Friedrich Pukelsheim Representation 54 (2018) 147–158
arxiv,
pdf
Critical surface of the 1-2 model
with Zhongyang Li International Mathematics Research Notices 21 (2018) 6617–6672
arxiv,
pdf
Locality of connective constants
with Zhongyang Li Discrete Mathematics 341 (2018) 3483–3497
arxiv,
pdf
A 700-seat no-loss composition for the 2019 European Parliament, 2017
with F. Pukelsheim,
V. Ramírez González,
W. Słomczyński,
K. Życzkowski 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
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
Counting self-avoiding walks
with Zhongyang Li Accepted in Tsinghua
Lectures in Mathematics, 2017
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
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
2015
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
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 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
2010
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
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
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
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
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ed. H. Kesten,
Encyclopedia of Mathematical Sciences, vol. 110,
Springer, 2003, 73–123
arxiv,
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Rigidity of the interface in percolation and random-cluster models
with Guy Gielis Journal of Statistical Physics 109 (2002) 1–37
arxiv,
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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
2000
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
1995
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
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
Random walk on the infinite cluster of the percolation model,
with Harry Kesten and Yu Zhang Probability Theory and Related Fields 96 (1993) 33–44
pdf
Random graphical networks
in Networks and Chaos—Statistical and Probabilistic Aspects ed. O. E. Barndorff-Nielsen et al., Chapman and Hall, London, 1993, 288–301
pdf
On the asymptotic distribution of large prime factors
with P. J. Donnelly Journal of London Mathematical Society 47 (1993) 395–404
pdf
On the geometry of random Cantor sets and fractal percolation
with K. J. Falconer Journal of Theoretical Probability 5 (1992) 465–486;
correction in volume 7 (1994) 209–210
pdf
Weak convergence using higher-order cumulants
Journal of Theoretical Probability 5 (1992) 767–774
pdf
The asymptotics of random sieves
with R. R. Hall Mathematika 38 (1991) 285–302
pdf
Statistics of sieves and square-free numbers
Journal of London Mathematical Society 43 (1991) 1–11
pdf
The critical point of fractal percolation in three and more dimensions
with K. J. Falconer Journal of Physics A: Mathematical and General
24 (1991) L491–L494
pdf
Exponential decay for subcritical contact and percolation processes
with C. Bezuidenhout Annals of Probability 19 (1991) 984–1009
pdf
Strict monotonicity of critical points in percolation and ferromagnetic models
with M. Aizenman Journal of Statistical Physics 63 (1991) 817–835
pdf
Dynamic renormalization and continuity of the percolation transition in orthants
with D. J. Barsky and C. M. Newman in Spatial Stochastic Processes, A Festschrift in Honor of Ted Harris ed. K. S. Alexander and J. C. Watkins, Birkhäuser, Boston, 1991, 37–55
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Percolation in half spaces: equality of critical probabilities and continuity of the percolation probability
with D. J. Barsky and C. M. Newman Probability Theory and Related Fields} 90 (1991) 111–148
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
The supercritical phase of percolation is well behaved
with J. M. Marstrand Proceedings of the Royal Society (London), Series A, 430 (1990) 439–457
pdf
The critical contact process dies out
with C. Bezuidenhout Annals of Probability 18 (1990) 1462–1482, Special Invited Paper
pdf
1990
The correlation length for the high density phase of Bernoulli percolation
with J. T. Chayes, L. Chayes, H. Kesten, R. H. Schonmann Annals of Probability 17 (1989) 1277–1302
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On the uniqueness of the infinite cluster in the percolation model
with A. Gandolfi and L. Russo Communications in Mathematical Physics 114 (1988) 549–552
pdf
Superbranching processes and projections of random Cantor sets
with M. Dekking Probability Theory and Related Fields} 78 (1988) 335–355
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Long paths and cycles in a random lattice
in Random Graphs '85 ed. M. Karoński and Z. Palka, Annals of Discrete Mathematics 33,
North-Holland, Amsterdam, 1987, 69–76
pdf
Recent progress in percolation
Proceedings of First World Congress of Bernoulli Society, Tashkent 1986
ed. Yu. V. Prohorov and V. V. Sazonov, VNU
Science Press, Utrecht, 1987
pdf
Interacting particle systems and random media, an overview
International Statistical Review 55 (1987) 49–62
pdf
An exact threshold theorem for random graphs and the node-packing problem
Journal of Combinatorial Theory B 40 (1986) 187–195
pdf
Percolation processes and dimensionality
in Stochastic Spatial Processes ed. P. Tautu, Springer Lecture Notes in Mathematics no. 1212, 1986,
165–174
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On a conjecture of Hammersley and Whittington concerning bond percolation on subsets of the simple cubic lattice
Journal of Physics A:
Mathematical and General 18 (1985) L49–L52
pdf
The shortest-path problem for graphs with random arc-lengths
with A. M. Frieze Discrete Applied Mathematics 10 (1985) 57–77
pdf
Random flows: network flows and electrical flows through random media
in
Surveys in Combinatorics 1985 ed. I. Anderson, Cambridge University
Press, 1985, 59–96
pdf
Large deviations in subadditive processes and first-passage percolation
in
Particle Systems, Random Media, and Large Deviations ed. R. Durrett, American Mathematical Society Contemporary Mathematics Series 41,
1985, 175–194
pdf
Random spatial processes in physics: particle systems and random media
Bulletin of the International Statistical Institute (1985) 27.2
pdf
Random near-regular graphs and the node packing problem
with W. Pulleyblank Operations Research Letters 4 (1985) 169–174
pdf
Electrical networks with random resistances
in Random Graphs '83 ed. M. Karoński and A. Ruciński
Annals of Discrete Mathematics
28, North-Holland, Amsterdam, 1985, 125–136
pdf
The largest components in a random lattice
Studia Scientiarum
Mathematicarum Hungarica 20 (1985) 325–331
pdf
1985
Central limit theorems for associated random variables and the percolation model
with J. T. Cox Annals of Probability 12 (1984) 514–528
pdf
On the connectedness of a random graph
with M. Keane and J. M. Marstrand Mathematical Proceedings of Cambridge Philosophical Society 96 (1984) 151–166
pdf
First-passage percolation, network flows and electrical networks
with H. Kesten Zeitschrift für Wahrscheinlichkeitstheorie und verwandte
Gebiete 66 (1984) 335–366
pdf
Random electrical networks on complete graphs
with H. Kesten Journal of the London Mathematical Society 30 (1984) 171–192
pdf
Bond percolation on subsets of the square lattice, and the threshold
between one-dimensional and two-dimensional behaviour
Journal of Physics
A: Mathematical and General 16 (1983) 599–604
pdf
Random graphs
in Selected Topics in Graph Theory II ed. L. Beineke
and R. Wilson, Academic Press, London, 1983, 201–235
pdf
Flow in networks with random capacities
with D. J. A. Welsh Stochastics 7 (1982) 205–229
pdf
The maximal flow through a directed graph with random
capacities
with W.-C. S. Suen Stochastics 8 (1982) 153–159
pdf
On the differentiability of the number of clusters per vertex in the
percolation model
Journal of the London Mathematical Society} 23 (1981)
372–384
pdf
Central limit theorems for percolation models
with J. T. Cox Journal of Statistical Physics 25 (1981) 237–251
pdf
Critical sponge dimensions in percolation theory
Advances in Applied
Probability 13 (1981) 314–324
pdf
On taking up position in a group: A continuous-time
Markov model for biased random movement
with M. Treisman British Journal of Mathematical
and Statistical Psychology 33 (1980) 247–261
pdf
A linear cell-size dependent branching process
Stochastic Processes
and their Applications 10 (1980) 105–113
pdf
Random labelled trees and their branching networks
Journal of the
Australian Mathematical Society A 30 (1980) 229–237
pdf
1980
Multidimensional lattices and their partition functions
Oxford
Quarterly Journal of Mathematics 29 (1978) 141–157
pdf
The rank polynomials of large random lattices
Journal of the London
Mathematical Society 18 (1978) 567–575
pdf
An upper bound for the number of spanning trees of a graph
Discrete
Mathematics 16 (1976) 323–324
pdf
On the number of clusters in the percolation model
Journal of the London
Mathematical Society 13 (1976) 346–350
pdf
On colouring random graphs
with C. J. H. McDiarmid Mathematical
Proceedings of the Cambridge Philosophical Society} 77 (1975) 313–324
pdf
A non-Markovian birth process with logarithmic growth
Journal of
Applied Probability 12 (1975) 67–683
pdf
1975
Maximal solutions of the generalized subadditive inequality
with J. M. Hammersley in Stochastic Geometry ed. E. Harding and D. Kendall, Wiley,
1974, 270–284
pdf
Random graph theorems
Transactions of 7th Prague Conference on
Information Theory and Related Topics, 1974, 203–209
pdf
A generalization of a theorem of Kleitman and Milner
Bulletin of the
London Mathematical Society 5 (1973) 157–158
pdf
A theorem about random fields
Bulletin of the London Mathematical Society
5 (1973) 81–84
pdf
1970
Software
Toolbox hinge generator with Hugo Grimmett (March 2025)
html
Bonus volumes
Percolation Theory for Mathematicians, by
Harry Kesten, 1982
pdf
Introspective Classification for Robot
Perception and Decision Making, by
Hugo Grimmett DPhil Thesis, University of Oxford, 2016
pdf
