L
Lucas Gerin
Researcher at École Polytechnique
Publications - 46
Citations - 363
Lucas Gerin is an academic researcher from École Polytechnique. The author has contributed to research in topics: Random permutation & Cellular automaton. The author has an hindex of 9, co-authored 43 publications receiving 284 citations. Previous affiliations of Lucas Gerin include University of Paris & Chicago Metropolitan Agency for Planning.
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The Brownian limit of separable permutations
TL;DR: In this paper, the authors study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations, and describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in terms of the Brownian excursion.
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Efficient estimation of the cardinality of large data sets
Philippe Chassaing,Lucas Gerin +1 more
TL;DR: In this paper, an optimal estimation of the number of distinct elements in a large sequence of words is proposed, using Kullback information and estimation theory, under strong constraints coming from the analysis of large data bases.
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Universal limits of substitution-closed permutation classes
Frédérique Bassino,Mathilde Bouvel,Valentin Féray,Lucas Gerin,Mickaël Maazoun,Adeline Pierrot +5 more
TL;DR: In this paper, the authors consider uniform permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons, which is an elementary one-parameter deformation of the limit of uniform separable permutations.
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On the convergence of population protocols when population goes to infinity
TL;DR: In this paper, the authors studied the convergence of population protocols when the size of the population goes to infinity and obtained an asymptotic development for a particular protocol for which they even obtained an exponential convergence.
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Universal limits of sunstitution-closed permutation classes
Frédérique Bassino,Mathilde Bouvel,Valentin Féray,Lucas Gerin,Mickaël Maazoun,Adeline Pierrot +5 more
TL;DR: In this article, the convergence of random permutons through convergence of their expected pattern densities is characterized by using the substitution tree encoding of permutations and performing singularity analysis on the tree series.