Fredrik Viklund

KTH Royal Institute of Technology

Convergence of loop-erased walk in the natural parametrization

Probability Seminar

10th November 2017, 3:30 pm – 4:30 pm
Main Maths Building, SM4

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 the Schramm-Loewner evolution with parameter 2 (SLE(2)), as curves viewed up to reparametrization. It is however more natural to view the discrete curve as parametrized by (renormalized) length and it has been believed for some time 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. I will discuss recent joint works with Greg Lawler (Chicago) that prove this stronger convergence, focusing on explaining the main ideas of the argument.

Fredrik Viklund


I am an associate professor in the Department of Mathematics, KTH Royal Institute of Technology and a Wallenberg Academy Fellow. I am partially supported by the Swedish Research Council (VR) and the Goran Gustafsson foundation.

Prior to returning to KTH, I was a Simons Fellow and Ritt Assistant Professor at Columbia University and then an associate professor at Uppsala University. While at Columbia I was partially supported by the National Science Foundation (NSF). I received my Ph.D. in 2010 from KTH. My advisor was Michael Benedicks.

Organisers: Benjamin Lees, Jessica Jay

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