In probability theory, 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 Charles Loewner's differential equation with Brownian motion as input. It was discovered by Oded Schramm (2000) as a conjectured scaling limit of the planar uniform spanning tree (UST) and the planar loop-erased random walk (LERW) pr...
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In probability theory, 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 Charles Loewner's differential equation with Brownian motion as input. It was discovered by Oded Schramm (2000) as a conjectured scaling limit of the planar uniform spanning tree (UST) and the planar loop-erased random walk (LERW) probabilistic processes, and developed by him together with Greg Lawler and Wendelin Werner in a series of joint papers.
Schramm–Loewner evolution is conjectured or proved to be the scaling limit of various critical percolation models, and other stochastic processes in the plane.
If D is a simply connected, open complex domain not equal to C, and γ is a simple curve in D starting on the boundary (a continuous function with γ(0) on the boundary and γ((0, ∞)) in D), then for each t ≥ 0, the complement Dt of γ([0, t]) is simply connected and...
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