Publications supported by RaG

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

1. A characterisation of the Gaussian free field
   Nathanael Berestycki, Ellen Powell, Gourab Ray
2. Weighted self-avoiding walks
   Geoffrey Grimmett and Zhongyang Li
3. On influence and compromise in two-tier voting systems
   Geoffrey Grimmett
4. Spin systems from loop soups
   Tim van de Brug, Federico Camia, Marcin Lis
5. Six-vertex model and Schramm–Loewner evolution
   Kenyon R, Miller J, Sheffield S, Wilson DB
   Physical Review E 95 (2017) 052146
6. Circle patterns and critical Ising models
   Marcis Lis
7. On the double random current nesting field
   Hugo Duminil-Copin, Marcis Lis
8. Probability on Graphs
   Cambridge University Press, 2nd edition, 2018
   Geoffrey Grimmett
9. The parabolic Anderson model on Riemann surfaces
   Antoine Dahlqvist, Joscha Diehl, Bruce Driver
10. Self-avoiding walks and connective constants
    Geoffrey Grimmett, Zhongyang Li
11. The Rohde-Schramm theorem, via the Gaussian free field
    Nathanael Berestycki, Henry Jackson
12. Yang-Mills measure and the master field on the sphere
    Antoine Dahlqvist, James Norris
13. Lozenge tiling dynamics and convergence to the hydrodynamic equation
    B. Laslier, F. L. Toninelli
14. A unimodular Liouville hyperbolic souvlaki --- an appendix to [arXiv:1603.06712]
    Gabor Pete, Gourab Ray
15. The planar Ising model and total positivity
    M. Lis
    Journal of Statistical Physics 166 (2017) 72–89
16. Hyperbolic and parabolic unimodular random maps
    Omer Angel, Tom Hutchcroft, Asaf Nachmias, Gourab Ray
17. Classification of scaling limits of uniform quadrangulations with a boundary
    Erich Baur, Gregory Miermont, Gourab Ray
18. Cubic graphs and the golden mean
    Geoffrey Grimmett, Zhongyang Li
19. Random Hermitian matrices and Gaussian multiplicative chaos
    Nathanael Berestycki, Christian Webb, Mo Dick Wong
20. A note on dimers and T-graphs
    Nathanael Berestycki, Benoit Laslier, Gourab Ray
21. Liouville quantum gravity and the Brownian map III: the conformal structure is determined
    Jason Miller, Scott Sheffield
22. Hydrodynamic limit equation for a lozenge tiling Glauber dynamics
    B. Laslier, F. L. Toninelli
23. Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding
    Jason Miller, Scott Sheffield
24. The work of Lucio Russo on percolation
    Geoffrey Grimmett
    Mathematics and Mechanics of Complex Systems 4 (2016) 199–211
25. Universality of fluctuations in the dimer model
    Nathanael Berestycki, Benoit Laslier, Gourab Ray
26. CLE percolations
    Jason Miller, Scott Sheffield, Wendelin Werner
27. The half plane UIPT is recurrent
    Omer Angel and Gourab Ray
    Probability Theory and Related Fields (2017)
28. The generalized master fields
    Guillaume Cebron, Antoine Dahlqvist, Franck Gabriel
29. Universal constructions for spaces of traffics
    Guillaume Cebron, Antoine Dahlqvist, Camille Male
30. Correlation inequalities for the Potts model
    Geoffrey Grimmett
    Mathematics and Mechanics of Complex Systems 4 (2016) 327–334
31. Existence of self-accelerating fronts for a non-local reaction-diffusion equations
    Nathanael Berestycki, Clement Mouhot, Gael Raoul
32. Bipolar orientations on planar maps and SLE12
    Richard Kenyon, Jason Miller, Scott Sheffield, David B. Wilson
33. Conformal weldings of random surfaces: SLE and the quantum gravity zipper
    Scott Sheffield
34. Self-avoiding walks and amenability
    Geoffrey Grimmett and Zhongyang Li
    The Electronic Journal of Combinatorics 24 (2107) paper P4.38
35. Critical surface of the hexagonal polygon model
    Geoffrey Grimmett and Zhongyang Li
    Journal of Statistical Physics 163 (2016) 733–753
36. The 1-2 model
    Geoffrey Grimmett and Zhongyang Li
    Proceedings of 6th Ahlfors–Bers symposium
    Contemporary Mathematics, AMS
37. Liouville quantum gravity and the Brownian map I: The QLE(8/3,0) metric
    Jason Miller, Scott Sheffield
38. An elementary approach to Gaussian multiplicative chaos
    Nathanael Berestycki
    Electronic Communications in Probability 22 (2017) paper 27
39. Critical surface of the 1-2 model
    Geoffrey Grimmett and Zhongyang Li
    International Mathematics Research Notices (2017)
40. An axiomatic characterization of the Brownian map
    Jason Miller, Scott Sheffield
41. Liouville quantum gravity spheres as matings of finite-diameter trees
    Jason Miller, Scott Sheffield
42. Small-time fluctuations for the bridge of a sub-Riemannian diffusion
    Ismael Bailleul, Laurent Mesnager, James Norris
    Annals of Probability
43. Random walks on the random graph
    Nathanael Berestycki, Eyal Lubetzky, Yuval Peres, Allan Sly
44. Near-critical spanning forests and renormalization
    Stéphane Benoist, Laure Dumaz, Wendelin Werner
45. Critical exponents on Fortuin–Kasteleyn weighted planar maps
    Nathanael Berestycki, Benoit Laslier, Gourab Ray
    Communications in Mathematical Physics
46. Random walks on stochastic hyperbolic half planar triangulations
    O. Angel, A. Nachmias, G. Ray
    Random Structures Algorithms 49 (2016) 213–234
47. Unimodular Hyperbolic Triangulations: Circle Packing and Random Walk
    Omer Angel, Tom Hutchcroft, Asaf Nachmias, Gourab Ray
48. Spectral curves of periodic Fisher graphs
    Zhongyang Li
    Journal of Mathematical Physics 55, 123301 (2014)
49. Conformal invariance of dimer heights on isoradial double graphs
    Zhongyang Li
    Annales de l'Institut Henri Poincare D
50. Connective constants and height functions of Cayley graphs
    Geoffrey Grimmett and Zhongyang Li
    Transactions of the AMS 369 (2017) 5961–5980
51. Equivalence of Liouville measure and Gaussian free field
    Nathanael Berestycki, Scott Sheffield, Xin Sun
52. Cutoff for conjugacy-invariant random walks on the permutation group
    Nathanael Berestycki, Bati Sengul
53. Locality of connective constants
    Geoffrey Grimmett and Zhongyang Li
54. The Potts and random-cluster models
    Geoffrey Grimmett
55. Measure solutions for the Smoluchowski coagulation-diffusion equation
    James Norris
56. Cyclic polynomials in two variables
    Catherine Bénéteau, Greg Knese, Lukasz Kosiński, Constanze Liaw, Daniel Seco, Alan Sola
    Transactions of the AMS 368 (2016) 8737–8754
57. Surprise probabilities in Markov chains
    James Norris, Yuval Peres, Alex Zhai
    Combinatorics, Probability and Computing 26 (2017) 603–627
58. From Sine kernel to Poisson statistics
    Romain Allez, Laure Dumaz
    Electronic Journal of Probability 19 (2014) 1–25
59. KPZ formula derived from Liouville heat kernel
    Nathanael Berestycki, Christophe Garban, Remi Rhodes, Vincent Vargas
    Journal of the London Mathematical Society 94 (2106) 186–208
60. A consistency estimate for Kac's model of elastic collisions in a dilute gas
    James Norris
    Advances in Applied Probability 26 (2016) 1029–1081
61. Random matrices in non-confining potentials
    Romain Allez, Laure Dumaz
    Journal of Statistical Physics 160 (2015) 681–714
62. Tracy-Widom at high temperature
    Romain Allez, Laure Dumaz
    Journal of Statistical Physics 156 (2014) 1146–1183
63. Criticality, universality, and isoradiality
    Geoffrey Grimmett
    Proceedings of the 2014 ICM, Seoul
64. Cyclicity in Dirichlet-type spaces and extremal polynomials II: functions on the bidisk
    Catherine Bénéteau, Alberto Condori, Constanze Liaw, Daniel Seco, Alan Sola
    Pacific Journal of Mathematics 276 (2015) 35–58
65. Small-particle limits in a regularized random Laplacian growth model
    Fredrik Johansson Viklund, Alan Sola, Amanda Turner
    Commun. Math. Phys. 334 (2015) 331–366
66. Discrete complex analysis and T-graphs
    Zhongyang Li
67. Coalescing Brownian flows: a new approach
    Nathanael Berestycki, Christophe Garban, Arnab Sen
    Annals of Probability 43 (2015) 3177–3215
68. Extendable self-avoiding walks
    Geoffrey Grimmett, Alexander Holroyd, Yuval Peres
    Annales de l'Institut Henri Poincare D: CPI 1 (2014) 61–75
69. Condensation of a two-dimensional random walk and the Wulff crystal
    Nathanael Berestycki, Ariel Yadin
70. The shape of multidimensional Brunet-Derrida particle systems
    Nathanael Berestycki, Lee Zhuo Zhao
    Annals of Applied Probability
71. Counting self-avoiding walks
    Geoffrey Grimmett, Zhongyang Li
72. Percolation of finite clusters and infinite surfaces
    Geoffrey Grimmett, Alexander Holroyd, Gady Kozma
    Mathematical Proceedings of the Cambridge Philosophical Society 156 (2014) 263–279
73. Diffusion in planar Liouville quantum gravity
    Nathanael Berestycki
    Ann Inst H Poincaré B 51 (2015) 947–964
74. Cyclicity in Dirichlet-type spaces and extremal polynomials
    Catherine Bénéteau, Alberto Condori, Constanze Liaw, Daniel Seco, Alan Sola
    Journal d'Analyse Mathématique 126 (2015) 259–286
75. Expected discrepancy for zeros of random polynomials
    Igor Pritsker, Alan Sola
    Proceedings of the American Mathematical Society 142 (2014) 4251–4263
76. Elementary examples of Loewner chains generated by densities
    Alan Sola
    Annales Universitatis Mariae Curie-Sklodowska A 67 (2013) 83–101
77. Strict inequalities for connective constants of transitive graphs
    Geoffrey Grimmett, Zhongyang Li
    SIAM Journal of Discrete Mathematics 28 (2014), 1306–1333.
78. Critical branching Brownian motion with absorption: particle configurations
    Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg
    Annales IHP (B) 51 (2015) 1215&ndash'1250
79. Critical branching Brownian motion with absorption: survival probability
    Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg
    Probab. Theor. Rel. Fields 160 (2014) 489–520
80. Diffusivity of a random walk on random walks
    Emmanuel Boissard, Serge Cohen, Thibault Espinasse, James Norris
    Random Struct. Alg. 47 (2015) 267–283
81. Uniqueness of the infinite homogeneous clusters in 1-2 model
    Zhongyang Li
    Electron. Commun. Probab. 19 (2014), Paper 23, 8 pp.
82. Bounds on connective constants of regular graphs
    Geoffrey Grimmett, Zhongyang Li
    Combinatorica 35 (2015) 279–294
83. Self-avoiding walks and the Fisher transformation
    Geoffrey Grimmett, Zhongyang Li
    European Journal of Combinatorics 20 (2013), Paper P47, 14 pp
84. Influence in product spaces
    Geoffrey Grimmett, Svante Janson, James Norris
    Advances in Applied Probability (2016)
85. A small-time coupling between Lambda-coalescents and branching processes
    Julien Berestycki, Nathanael Berestycki, Vlada Limic
    Ann. Appl. Probab. 24 (2014) 449–475
86. The genealogy of branching Brownian motion with absorption
    Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg
    Ann. Probab., 41, 527–618 (2013)
87. Percolation since Saint-Flour
    Geoffrey Grimmett, Harry Kesten
    In Percolation Theory at Saint-Flour, Springer, 2012, pages ix--xxvii.
88. Cycle structure of the interchange process and representation theory
    Nathanael Berestycki, Gady Kozma
    Bull. Soc. Math. France
89. Galton–Watson trees with vanishing martingale limit
    Nathanael Berestycki, Nina Gantert, Peter Moerters, Nadia Sidorova
    J. Stat. Phys. 155 (2014) 737–762
90. Critical temperature of periodic Ising models
    Zhongyang Li
    Communications in Mathematical Physics 315 (2012) 337–381
91. Bond percolation on isoradial graphs: criticality and universality
    Geoffrey Grimmett, Ioan Manolescu
    Probability Theory and Related Fields 159 (2014) 273–327
92. Asymptotic sampling formulae for Lambda-coalescents
    Julien Berestycki, Nathanael Berestycki, Vlada Limic
    Ann. Inst. H. Poincaré B 50 (2014) 715–731
93. 1-2 model, dimers, and clusters
    Zhongyang Li
    Electronic Journal of Probability 19 (2014) Paper 48.
94. Large scale behaviour of the spatial Lambda-Fleming-Viot process
    Nathanael Berestycki, Alison Etheridge, Amandine Veber
    Ann. Inst. H. Poincaré B (2013) 49, 374–401 (2013)
95. Hastings–Levitov aggregation in the small-particle limit
    James Norris, Amanda Turner
    Commun. Math. Phys. (2012) 316, 809–841
96. Weak convergence of the localized disturbance flow to the coalescing Brownian flow
    James Norris, Amanda Turner
    Annals of Probability 43 (2015) 935–970
97. Three theorems in discrete random geometry
    Geoffrey Grimmett
    Probability Surveys 8 (2011) 403–441,
98. Universality for bond percolation in two dimensions
    Geoffrey Grimmett, Ioan Manolescu
    Annals of Probability 41 (2013) 3261–3283
99. Inhomogeneous bond percolation on square, triangular, and hexagonal lattices
    Geoffrey Grimmett, Ioan Manolescu
    Annals of Probability 41 (2013) 2990–3025
100. Cluster detection in networks using percolation
     Geoffrey Grimmett, Ery Arias-Castro
     Bernoulli 19 (2013) 676–719