The versions provided below may present (very) slight differences with the published versions. If some links do not work, please, tell me!!

Artistic illustration

- The Brownian map
- The Brownian tree
- The Brownian snake
- The hairy snake

Artist: Emmanuelle Marckert (a sister of mine)

On this page , are provided simulations of ...quadrangulations, trees, snakes, Brownian processes (motion, excursion, bridge, meander), their local time process at time 1, loop erased random walks, uniform spanning tree of the grid, Bessel processes

Publications Coauthors Web Pages

Note on the density of ISE and a related diffusion
With Guillaume Chapuy
arxiv 2210.10159

Almost triangular Markov chains on N
With Luis Fredes

Models of random subtrees of a graph
With Luis Fredes
arxiv 2102.12738

Growing random uniform d-ary trees
Version.pdf arxiv:2105.05513
Annals of Combinatorics (2022). Journal page

Parametrised branching processes: a functional version of Kesten & Stigum theorem
With Cécile Mailler
Stochastic Processes and their Applications, Volume 152, October 2022, Pages 339-377

A combinatorial proof of Aldous--Broder theorem for general Markov chains
With Luis Fredes
hal-03142148 Random Structures and Algorithms, 2022

Iterated foldings of discrete spaces and their limits: candidates for the role of Brownian map in higher dimensions
With Luca Lionni
Mathematical Physics, Analysis and Geometry, 24, Article number: 39 (2021)

Around Sylvester's question in the plane
With Said Rahmani
Mathematika, 67, Issue4, 2021, 860-884.

Invariant measures of discrete interacting particle systems: Algebraic aspects
With Luis Fredes
ESAIM: PS, ESAIM: PS 24 (2020) 526–580

The combinatorics of the colliding bullets problem
With Nicolas Broutin
Random stuctures and algorithms, Volume56, Issue2 March 2020

Directed, cylindric and radial Brownian webs
With David Coupier and Viet Chi Tran
Electronic Journal of Probability, Volume 24 (2019), paper no. 20, 48 pp.

A new combinatorial representation of the additive coalescent
With Minmin Wang
Random Structures and Algorithms, Volume54, Issue2 March 2019

Measure-valued Polya processes
With Cécile Mailler
link to the paper
Electron. J. Probab. Volume 22 (2017), paper no. 26, 33 pp.

Processes iterated ad libitum
With Jérôme Casse
Stochastic Processes and their Applications, Elsevier, 2016, Volume 126 (11), pp.5.

The probability that n random points in a disk are in convex position
version pdf
Brazilian Journal of Probability and Statistics 2017, Vol. 31, No. 2, 320-337.

A new encoding of coalescent processes. Applications to the additive and multiplicative cases
With Nicolas Broutin
Probability theory and related fields, 2016, 166 (1), pp.515--552.

Markovianity of the invariant distribution of probabilistic cellular automata on the line
With Jérôme Casse
Stochastic processes and their applications, Volume 125, Issue 9, September 2015, Pages 3458-3483

Compact convexes of the plane and probability theory
With David Renault
version pdf
ESAIM: Probability and Statistics, Volume 18, Jan. 2014, pp 854-880

A functional central limit theorem for the partial sums of sorted i.i.d. random variables
With David Renault version pdf arXiv:1302.6926
Unpublished (2013)

A natural stochastic extension of the sandpile model on a graph
With Yao-ban Chan and Thomas Selig
JCTA , Volume 120, Issue 7, September 2013, Pages 1913–1928

Many empty triangles have a common edge
With Imre Bárány and Matthias Reitzner version.pdf
Discrete and Computational Geometry, Vol 50, Issue 1,p 244-252 (2013)

Directed animals, quadratic and rewriting systems
Electron. Journal Comb. 19, No. 3, Research Paper P45, 31 p., electronic only (2012).

Asymptotic of trees with a prescribed degree sequence and applications
With Nicolas Broutin version pdf arXiv:1110.5203
Random Structures and Algorithms, Volume 44, Issue 3, pages 290–316, May 2014 (online sept.2012)

Asymptotic of geometrical navigation on a random set of points of the plane
With Nicolas Bonichon version pdf arXiv:1009.4679
Advances in Applied Probability Volume 43, Number 4 (2011), 899-942.

The CRT is the scaling limit of unordered binary trees
With Grégory Miermont
arXiv: 0902.4570 version pdf
Random Structures and Algorithms Volume 38, Issue 4, July 2011, Pages: 467–501,

On the reduction of a random basis
With A. Akhavi and A. Rouault
version pdf) version ps.gz) ESAIM: PS 13 (2009) p. 437-458

Short version : Analco, Proceedings of the ninth workshop on algorithm engineering and experiments and the fourth workshop on analytic algorithmics and combinatorics, edited by David Applegate, Gerth Stoling Brodal, Daniel Panario and Robert Sedgewick,New Orleans LA, SIAM (2007)

Uniform bounds for the exponential moments of the maximum of Dyck paths
With O. Khorunzhiy,
arXiv:0902.1229 version pdf
Electronic Communications in Probability, (2009) paper 33, 327-333

Election algorithms with random delays in trees
With N. Saheb-Djahromi and A. Zemmari, version pdf
PSAC 2009, to appear in DMTCS

A symmetry property of some harmonic algebraic curves
With J.C. Aval version pdf arXiv:0805.2016

Some families of increasing planar maps
With M. Albenque version pdf arXiv:0712.0593
Electronic journal of probability, (2008), paper 56, 1624-1671.

One more approach to the convergence of the empirical process to the Brownian bridge version pdf Arxiv : abs/0710.3296
Electronic journal of Statistics, Vol.2. (2008) p.118-126

Directed Animals and Gas Models Revisited
With Y. Le Borgne version pdf Arxiv: math.PR/0611194
The Electronic Journal of Combinatorics , R71, (2007)

The lineage process in Galton-Watson trees and globally centered discrete snakes version pdf Arxiv : math.PR/0606338
Annals of Applied Probability, Vol. 18, No. 1, 209-244, (2007)

Quasi-Optimal Energy-Efficient Leader Election Algorithms in Radio Networks
With C. Lavault and V. Ravelomanana. version pdf
Information and Computation, Vol. 205, Issue 5, May (2007), p. 679-693

Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks
With J.M. Labarbe. version pdf Arxiv : math.PR/0601624
Electronic journal of probability, (2007), p. 229-261.

Invariance principles for random bipartite planar maps
With G. Miermont
(version pdf)Arxiv : math.PR/0504110
The Annals of probability, (2007), Vol. 35, No.5, p. 1642-1705

Limit of Normalized Quadrangulations: the Brownian map
With A. Mokkadem,
(not the last version pdf Arxiv math.PR/0403398
The Annals of probability, Vol. 34, No.6, p. 2144-2202, (2006)

Martingales and Profile of Binary Search Trees
With B. Chauvin, T. Klein, A. Rouault version pdf Long version: Arxiv : math.PR/0410211
Electronic journal of probability, 10 (2005), no. 12, p. 420--435

Convergence of Discrete Snakes
With S. Janson version pdf
Journal of theoretical probability, 18, No. 3 , 615-- 645 (2005)

Reinforced weak convergence of stochastic processes
With Michael Drmota
version ps.gz version pdf
Statistics Probability Letters, Vol. 71, Issue 3, 1 March (2005), Pages 283-294

The rotation correspondence is asymptotically a dilatation version pdf
Random Structures and Algorithms Vol. 24, Issue 2, (2004), p. 118-132

States spaces of the snake and of its tour -- Convergence of the discrete snake
With A. Mokkadem version pdf
Journal of theoretical probability, Vol. 16, No. 4, October (2003), p.1015-1046.

Ladder variables, Internal structure of Galton-Watson trees and Finite branching random walks
With A. Mokkadem. version pdf
Journal of Applied Probability, 40.3, 671- 689, (2003)

A Stochastically Quasi-Optimal Search Algorithm for the Maximum of the Simple Random Walk
With P. Chassaing and M. Yor.
version ps.gz version pdf
Annals of Applied Probability, (2003) p. 1264-1295, vol 13, no. 4.

The depth first processes of Galton-Watson trees converge to the same Brownian excursion
With A. Mokkadem. version pdf
The Annals of probability, Vol. 31, No. 3 - July, p. 1655-1678 (2003).

Non-crossing Trees are Almost Conditioned Galton-Watson trees
With Alois Panholzer
version ps.gz version pdf
Random Structures and Algorithms, Vol 20.1, (2002), p.115-125

Parking with density
version ps.gz version pdf
Random Structures and Algorithms, Vol 18, 4, p.364-380, (2001).

Parking functions, empirical processes and the width of rooted labeled trees
With P. Chassaing.
version ps.gz version pdf
The Electronic Journal of Combinatorics 8 (2001), R14.

The height and width of simple trees
With P. Chassaing and M. Yor.
version ps.gz version pdf
Mathematics and Computer Science : Algorithms, Trees, Combinatorics and Probabilities (Versailles 2000), p. 17-30. Editors : D. Gardy, A. Mokkadem - Birkhauser

The contour of size n general planar tree
version ps.gz version pdf
Unpublished (2000)

these (PHD Thesis)
(version ps.gz) (version pdf)

(version ps.gz) (version pdf)


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