Grégory Miermont

Unité de Mathématiques Pures et Appliquées
École Normale Supérieure de Lyon
46, allée d'Italie
69364 Lyon Cedex 07
France


Courrier électronique :
Bureau : M7.406
Téléphone : (+33) 4 72 72 84 21
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Research

My research topics are: random trees, large random maps, coalescence and fragmentation processes, stochastic calculus.

People with whom I had the pleasure to collaborate: Louigi Addario-Berry, David Aldous, Omer Angel, Erich Baur, Olivier Bernardi, Jérémie Bettinelli, Julien Berestycki, Jean Bertoin, Jérémie Bouttier, Nicolas Broutin, Xinxin Chen, Nicolas Curien, Léo Dort, Emmanuel Guitter, Bénédicte Haas, Jean-François Le Gall, Christina Goldschmidt, Markus Heydenreich, Remco van der Hofstad, Tim Hulshof, Emmanuel Jacob, Brett Kolesnik, Jean-François Marckert, Laurent Ménard, Jim Pitman, Gourab Ray, Loïc Richier, Jason Schweinsberg, Sanchayan Sen, Mathilde Weill, Matthias Winkel.

Preprints

  1. A large deviation principle for the normalized excursion of alpha-stable Lévy processes without negative jumps (2023).
    With Léo Dort and Christina Goldschmidt. arxiv:2310.14833

  2. Compact Brownian surfaces II. Orientable surfaces (2022).
    With Jérémie Bettinelli.
    arxiv:2212.12511

  3. On quasi-polynomials counting planar tight maps (2022).
    With Jérémie Bouttier and Emmanuel Guitter.
    arxiv:2203.14796

  4. Backbone scaling limit of the high-dimensional IIC (2013).
    With Markus Heydenreich, Remco van der Hofstad and Tim Hulshof.
    arXiv:1301.3486
    (Withdrawn because certain correction terms that arise in the Lace expansion of Section 3 were not identified and taken into account in the subsequent derivation. A new version with these correction terms included is in preparation)

Publications

  1. Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants
    With Jérémie Bouttier and Emmanuel Guitter
    Annales Henri Lebesgue 5, 1035--1110 (2022)

  2. On breadth-first constructions of scaling limits of random graphs and random unicellular maps
    With Sanchayan Sen
    Random Structures Algorithms 61, no.4, 803--843 (2022)

  3. Classification of scaling limits of uniform quadrangulations with a boundary
    With Erich Baur and Gourab Ray
    Ann. Probab. 47, no.6, 3397--3477 (2019)

  4. A Boltzmann approach to percolation on random triangulations
    With Olivier Bernardi and Nicolas Curien
    Canad. J. Math., 71 no. 1, 1--43 (2019).
    Here are the Maple sessions for bond percolation and site percolation

  5. On the stability of geodesics in the Brownian map.
    With Omer Angel and Brett Kolesnik.
    Ann. Probab., 45, n.5, 3451--3479 (2017).

  6. The scaling limit of the minimum spanning tree of the complete graph.
    With Louigi Addario-Berry, Nicolas Broutin and Christina Goldschmidt.
    Ann. Probab., 45, n.5, 3075--3144 (2017).

  7. Long Brownian bridges in hyperbolic spaces converge to Brownian trees.
    With Xinxin Chen
    Electron. J. Probab. 22, paper no. 58, 15pp., (2017)

  8. Compact Brownian surfaces I. Brownian disks.
    With Jérémie Bettinelli.
    Probability Theory and Related Fields 167 (3), 555--614 (2017)

  9. Geodesic rays in the uniform infinite half-planar quadrangulation return to the boundary.
    With Erich Baur and Loïc Richier.
    ALEA Lat. Am. J. Probab. Math. Stat. 13 (2), 1123--1149 (2016)

  10. Uniform infinite planar quadrangulations with a boundary.
    With Nicolas Curien.
    Random Structures Algorithms 47 (1), 30--58 (2015)

  11. The Scaling Limit of Uniform Random Plane Maps, via the Ambjørn-Budd Bijection
    With Jérémie Bettinelli and Emmanuel Jacob.
    Electron. J. Probab. 19, paper 73, 1--16 (2014)

  12. The cut-tree of large Galton-Watson trees and the Brownian CRT
    With Jean Bertoin.
    Ann. Appl. Probab. 23 (4), 1469--1493 (2013).

  13. The Brownian map is the scaling limit of uniform random plane quadrangulations
    Acta Math. 210, 319--401 (2013)

  14. The Brownian Cactus I. Scaling limits of discrete cactuses
    With Nicolas Curien and Jean-François Le Gall.
    Ann. Inst. Henri Poincaré (B) 49 (2), 340--373 (2013).

  15. A view from infinity of the Uniform Infinite Planar Quadrangulation
    With Nicolas Curien and Laurent Ménard.
    ALEA, Lat. Am. J. Probab. Math. Stat. 10 (1), 45--88 (2013).

  16. Scaling limits of Markov branching trees,
    With applications to Galton-Watson and random unordered trees.
    With Bénédicte Haas.
    Ann. Probab. 40, n.6, 2589--2666 (2012).

  17. Self-similar scaling limits of non-increasing Markov chains.
    With Bénédicte Haas.
    Bernoulli 17(4), 1217--1247 (2011).

  18. The CRT is the scaling limit of unordered binary trees.
    With Jean-François Marckert
    Random Structures Algorithms 38, n.4, 467--501 (2011).

  19. Scaling limits of random planar maps with large faces
    With Jean-François Le Gall.
    Ann. Probab., 39, n.1, 1--69 (2011).

  20. Tessellations of random maps of arbitrary genus
    Ann. Sci. Éc. Norm. Supér. 42, fascicule 5, 725--781 (2009).
    Transparents (slides)

  21. Invariance principles for spatial multitype Galton-Watson trees.
    Ann. Inst. Henri Poincaré (B) 44, 1128--1161 (2008).

  22. Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models
    With Bénédicte Haas, Jim Pitman and Matthias Winkel.
    Ann. Probab. 36, 1790--1837 (2008).

  23. On the sphericity of scaling limits of random planar quadrangulations
    Elect. Comm. Probab. 13, 248--257 (2008).
    Transparents (slides)

  24. Radius and profile of random planar maps with faces of arbitrary degrees
    With Mathilde Weill.
    Electron. J. Probab. 13, 79--106 (2008).

  25. Invariance principles for random bipartite planar maps.
    (initialement intitulé Invariance principles for labeled mobiles and bipartite planar maps).
    With Jean-François Marckert.
    Ann. Probab. 35, n.5, 1642--1705 (2007).

  26. Asymptotics in Knuth's parking problem for caravans.
    With Jean Bertoin.
    Random Structures and Algorithms, 29, n.1, 38--55 (2006).

  27. Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees.
    With David Aldous and Jim Pitman.
    Probab. Theory Relat. Fields, 133, n.1, 1--17 (2005).

  28. Self-similar fragmentations derived from the stable tree II: splitting at nodes.
    Probab. Theory Relat. Fields 131, n.3, 341--375 (2005).

  29. The exploration process of inhomogeneous continuum random trees, and an extension of Jeulin's local time identity.
    With David Aldous and Jim Pitman.
    Probab. Theory Relat. Fields 129, n.2, 182--218 (2004).
    Transparents (slides)

  30. Brownian Bridge Asymptotics for Random p-mappings.
    With David Aldous and Jim Pitman.
    Electr. J. Probab. 9, 37--56 (2004).

  31. The genealogy of self-similar fragmentations with negative index as a continuum random tree.
    With Bénédicte Haas.
    Electr. J. Probab. 9, 57--97 (2004). Transparents (slides).

  32. Self-similar fragmentations derived from the stable tree I: splitting at heights.
    Probab. Theory Relat. Fields 127, n. 3, 423--454 (2003).

  33. Self-similar fragmentations and stable subordinators.
    With Jason Schweinsberg.
    Sém. Prob. XXXVII, Lecture Notes in Maths. 1832, pp. 333--359, Springer, Berlin (2003).

  34. Ordered additive coalescents and fragmentations associated to Lévy processes with no positive jumps.
    Electr. J. Probab. 6, paper n.14, 1--33 (2001).

Book chapters/lecture notes

  1. Quelques aspects fractals des fragmentations aléatoires
    Avec Julien Berestycki, Jean Bertoin et Bénédicte Haas
    Chapter in the volume Quelques interactions entre analyse, probabilités et fractals
    Panoramas et Synthèses 32, Société Mathématique de France (2011).

  2. Scaling limits of random trees and planar maps
    With Jean-François Le Gall.
    Lecture notes for the Clay Mathematical Institute Summer School in Buzios
    July 11 - August 7, 2010.

Invited conference papers

  1. Random maps and continuum random 2-dimensional geometries
    6th European Congress of Mathematics, Kraków, 2-7 July, 2012, pp. 659--673, EMS Publishing House, 2014.

  2. On the scaling limit of random planar maps with large faces.
    With Jean-François Le Gall.
    XVIth International Congress on Mathematical Physics, 470--474, World Sci. Publ., Hackensack, NJ, 2010.

  3. Random maps and their scaling limits
    in C. Bandt, P. Mörters, M. Zähle (Eds.),
    Proceedings of the conference Fractal Geometry and Stochastics IV, Greifswald, 2008.
    Progress in Probability, Vol. 61, 197--224, Bikhaüser (2009).

  4. An invariance principle for random planar maps.
    in Fourth Colloquium in Mathematics and Computer Sciences CMCS'06, DMTCS Proceedings AG, 39--58 (2006), DMTCS, Nancy, France.
    Quelques errata.

Others


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