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

**Speaker:**Jérémie Bettinelli

**Location:**amphi. Germain (bât. Turing)

**Date:**Thu, 16 May 2019, 14:30-15:30

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.