Lucas Gerin: List of Publications (Back to the main page)

Thesis

Percolation, permutations, particules en interaction. Habilitation à diriger des recherches, Université Paris-Sud (2018).

Aspects probabilistes des automates cellulaires, et d'autres problèmes en informatique théorique. Thèse de mathématiques appliquées de l'Université Henri Poincaré (Nancy 1), dirigée par Philippe Chassaing (2008).

Articles

[24] Dense and nondense limits for uniform random intersection graphs. Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot.
Submitted.





[23] Scaling limit of graph classes through split decomposition. Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot.
Submitted.



My first Boltzmann sampler! Other simulations available on request.


[22] The Ulam-Hammersley problem for multiset permutations. Lucas Gerin.
To appear in Mathematical Proceedings of the Cambridge Philosophical Society (2024).



[21] Linear-sized independent sets in random cographs and increasing subsequences in separable permutations. Frédérique Bassino, Mathilde Bouvel, Michael Drmota, Valentin Féray, Lucas Gerin, Mickaël Maazoun, Adeline Pierrot.
Combinatorial Theory, vol.2 (2022), n.3.
[NB: We used computer algebra for some calculations in this paper, see the corresponding Notebook (html) extracted from SymPy.]





[20] Longest increasing paths with Lipschitz constraints. Anne-Laure Basdevant, Lucas Gerin.
Annales de l'IHP : Probabilités et Statistiques, vol.58 (2022) n.3, p.1849-1868.






[19] Scaling limits of permutation classes with a finite specification: a dichotomy. Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Mickaël Maazoun, Adeline Pierrot.
Advances in Mathematics, vol.405 (2022), Article 108513.

[NB: In order to find the specification of a given class and to solve the associated system, you can use the Sage/Jupyter notebook developed by M.Maazoun.]



(Simulation: M.Maazoun)


[18] Random cographs: Brownian graphon limit and asymptotic degree distribution. Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Mickaël Maazoun, Adeline Pierrot.
Random Structures and Algorithms, vol.60 (2022), p.166-200.




(Simulation: M.Maazoun)


[17] Universal limits of substitution-closed permutation classes. Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Mickaël Maazoun, Adeline Pierrot.
Journal of the European Mathematical Society vol.22 (2020), n.11, p.3565-3639.

New My recorded talk at Permutation Patterns 2021 about [17] and [13].



(Left: the Brownian case. Right: the stable case. Simulation: M.Maazoun)


[16] Longest increasing paths with gaps. Anne-Laure Basdevant, Lucas Gerin.
ALEA, vol.16 (2019) p.1141-1163.





[15] From Hammersley's lines to Hammersley's trees. Anne-Laure Basdevant, Lucas Gerin, Jean-Baptiste Gouéré, Arvind Singh.
Probability Theory and Related Fields, vol.171 (2018), n.1-2 p.1-51.



[14] Epidemic automaton and the Eden model: various aspects of robustness (book chapter). Lucas Gerin. In Probabilistic cellular automata. Theory, Applications and Future Perspectives. Editors: P.-Y. Louis, F.R.Nardi. Springer (Book Series: Emergence, Complexity and Computation) (2018).
Preliminary version available at HAL



[13] The Brownian limit of separable permutations. Frédérique Bassino, Mathilde Bouvel, Valentin Féray, Lucas Gerin, Adeline Pierrot.
Annals of Probability, vol.46 (2018) n.4, p.2134-2189.


(simulation: Carine Pivoteau)


[12] Discrete Hammersley's Lines with sources and sinks. Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin, Jean-Baptiste Gouéré.
ALEA, vol.XIII (2016), p.33-52.



[11] The Page-Rényi parking process. Lucas Gerin.
The Electronic Journal of Combinatorics, vol.22 (2015), n.4, P4.4.



[10] The shape of large balls in highly supercritical percolation. Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin, Jean-Baptiste Gouéré.
Electronic Journal of Probability, vol.19 (2014) article n.26, p.1-14.



[9] A branching-selection process related to censored Galton-Walton processes. Olivier Couronné, Lucas Gerin.
(Previous title : Survival time of a censored supercritical Galton-Watson process)
Annales de l'IHP : Probabilités et Statistiques, vol.50 (2014), n.1 p.84-94.





[8] Distances in the highly supercritical percolation cluster. Anne-Laure Basdevant, Nathanaël Enriquez, Lucas Gerin.
Annals of Probability, vol.41 (2013), n.6 p.4342-4358.





[7] On the algebraic numbers computable by some generalized Ehrenfest urns. Marie Albenque, Lucas Gerin.
Discrete Mathematics and Theoretical Computer Science, vol.14 (2012) n.2 p.271-284.

[6] Construction of a short path in high dimensional first-passage percolation. Olivier Couronné, Nathanaël Enriquez, Lucas Gerin.
Electronic Communications in Probability, vol.16 (2011) p.22-28.
Update (jan.2017) For the numerical constants, see the companion note Numerical lower and upper bounds for the Eden Model in high dimension, and the corresponding python code .

[5] Random sampling of lattice paths with constraints, via transportation. Lucas Gerin.
Proceedings of AofA'10, DMTCS Proceedings, vol.AM (2010) p.317-328.
[NB: Most of the results of this paper are in fact easy consequences of D.Wilson's paper "Mixing times of lozenge tiling and card shuffling Markov chains"]

[4] On the convergence of population protocols when population goes to infinity. Olivier Bournez, Philippe Chassaing, Johanne Cohen, Lucas Gerin, Xavier Koegler.
Applied Mathematics and Computation, vol.215 (2009) n.4 p.1340-1350.

[3] Examples of Fast and Slow Convergence of 2D Asynchronous Cellular Systems. Nazim Fatès, Lucas Gerin.
Journal of Cellular Automata, vol.4 (2009) n.4 p.323-337.

[2] Asynchronous Cellular Automata and Brownian Motion . Philippe Chassaing, Lucas Gerin
Proceedings of AofA'07. DMTCS Proceedings, vol.AH (2007) p.385-402.

[1] Efficient estimation of the cardinality of large data sets. Philippe Chassaing, Lucas Gerin.
Proceedings of 4th Colloquium on Mathematics and Computer Science . DMTCS Proceedings, vol.AG (2006) p.419-422.
The downloadable file (april 2011) is an extended (and much improved!) version of the published article.


Misc.

Problem 285 (Sheep and democracy) Feel free to send your solution to EMS Magazine!
EMS Magazine, vol.131 (2024), p.59.

How unfair is the unfair dodgem?
Recreational Mathematics Magazine, vol.10 (2023) n.17 p.41-50.

Random uniform permutations. Lecture notes for a mini-course (Master Paris-Saclay 2017 and Birzeit University, 2018)
Chinese restaurant process, Typical properties of random permutations, Size-bias phenomenon, Quicksort,...

Percolation et processus de croissance aléatoires. Notes pour un mini-cours (2h30 + 1h d'exercices) à l'Ecole thématique Journées ALEA (Marseille, 2013).