Loop-erased walks and natural parametrization (Fredrik Viklund, KTH Royal Institute of Technology, Sweden)

24.04.2017 15:15 – 17:15

Loop-erased random walk (LERW) is the random self-avoiding walk one gets after erasing the loops in the order they form from a simple random walk. Lawler, Schramm, and Werner proved that LERW in 2D converges in the scaling limit to SLE(2) as curves viewed up to reparametrization. It is however more natural to parametrize the discrete curve by (renormalized) length. In recent joint works with Greg Lawler we show that one then has convergence to SLE(2) equipped with the so-called natural parametrization, which in this case is the same as 5/4-dimensional Minkowski content. In the rst part I will introduce LERW and discuss some of its friends and basic properties, including a sharp one-point estimate. In the second part I will discuss the proof of convergence in the natural parametrization, focusing on explaining the main ideas of the argument. Based on joint works with Christian Benes (CUNY) and with Greg Lawler (Chicago).

Lieu

Room 17, Séminaire "Mathématique Physique"

entrée libre