Colloquium Mathematics - Nicolas Curien, Université Paris-Sud

As part of the Workshop On Randomness and Discrete Structures (WORDS2025) Nicolas Curien gives the following colloquium:

Title: Scaling limits of the Luczak-Winkler growth algorithm

Abstract:

Since the pioneering work of Aldous in the 1990s, it has been well established that large random trees converge towards a universal object: the Brownian tree. This object, which has become a pillar of modern probability, is a real random compact tree of fractal dimension 2. In this presentation, we will focus on different tree growth algorithms, such as the Rémy algorithm and the Luczak-Winkler algorithm. We will see how, by passing them to the limit, they give rise to diffusions taking values in the space of real trees, of which the Brownian tree constitutes the invariant law.