In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are generated by solving Loewner's differential equation with Brownian motion as input. The motivation for SLE was as a candidate for the scaling limit of "loop-erased random walk" (LERW) and, later, as a scaling limit of various other planar processes.
My question is about connections of SLE with theoretical physics, applications of SLE to theoretical physics and also applications of (other) theoretical physics to SLE. I will be happy to learn about various examples of such connections/applications preferably described as much as possible in a non-technical way.
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