From random walks to loops on random planar maps

Jeudi 26 novembre 2015 14:00-15:00 - Timothy Budd - Institut Niels Bohr, Université de Copenhague

Résumé : I will discuss random bipartite planar maps coupled to an O(n) loop model, and will show how a particular exploration process on such a map is related to a (partially) reflected random walk on the positive integers. Using the recent invariance principle of Bertoin and Kortchemski, I will show that the latter possesses a self-similar scaling limit given by a (partially) reflected stable process on the half-line, which has a simple Lamperti representation. Depending on the time, I will discuss how we can use this representation to learn something about the geometry of large loop-decorated maps.

Lieu : Salle 117-119

From random walks to loops on random planar maps  Version PDF