Laboratoire d'informatique de l'École polytechnique

The laboratory LIX

The abbreviation LIX stands for Laboratoire d'Informatique de l'Ecole polytechnique (Computer Science Laboratory of the École polytechnique), where the letter X represents the Polytechnique per French tradition. LIX is a mixed research unit (UMR 7161) consisting of two tutelles: the École polytechnique and the National Center for Scientific Research (CNRS). LIX falls under the jurisdiction of the INS2I division (which stands for the National Institute of Sciences of Information and their Interactions) of CNRS.

LIX director is Mireille Régnier and deputy director is Frank Valencia.

Sémin'Ouvert : « From the discrete world to the continuous world », par Jérémie Bettinelli (équipe Combi)

During this talk, I will present several accessible combinatorial structures known to converge toward interesting continuous limiting objects. Typically, if we possess, for a fixed integer n a finite number of combinatorial objects of "size" n, one may choose one uniformly at random and obtain a random combinatorial object. It often happens that, after scaling if necessary, this random discrete object converges toward a continuous object, which might be random or not. The most emblematic example of such a phenomenon is the convergence of a simple random walk, which go left, right, up, or down at each step with probability 1/4 (alternatively randomly wander in a typical American city), toward Brownian motion. This framework nicely intertwine combinatorics with probability theory and allows to wander between the discrete world and the continuous world.