Gastprof. Jean-François Marckert
Clemens Heuberger
WS 2009/2010
Die Vorlesung wird von Mitte Oktober bis Mitte November von J.-F. Marckert gehalten. Ab Mitte November wird sie (unter Ausdünnung des Stundenplans) von C. Heuberger gehalten.
The aim of combinatorics is to study the properties of discrete structures, starting by trying to count the number of objects of size n. An important question is to try to describe the objects of size n, when n is large: is it possible to say something about their limiting shape/behaviour, when n goes to infinity? During the last decades, some limiting behaviours has been proved for some particular cases; the limit is sometimes deterministic, sometimes random, and this after rescaling or not (for example, simple random walks with length n, have a limiting behaviour if rescaled by square root n). In this course, we will introduce the tools needed to prove an important archetype of these results (which has a lot of applications): suitably rescaled, trees converge in distribution to a continuum random object, named "the continuum random tree", introduced by Aldous (1991). Hence, the aim of this course is to make clear the notion of "convergence in distribution of combinatorial structures", and the by-products/benefits of such results. Some applications to analysis of algorithms will be given.