The dimension of the SLE curves

Vincent Beffara

The dimension of the SLE curves

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arxiv math/0211322 v3 pith:TZMDPXHZ submitted 2002-11-20 math.PR math.CV

Vincent Beffara This is my paper · ORCID

classification math.PRmath.CV

keywords dimensiongammakappacurvecurvesequalevolutiongenerating

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abstract

Let $\gamma$ be the curve generating a Schramm--Loewner Evolution (SLE) process, with parameter $\kappa\geq0$. We prove that, with probability one, the Hausdorff dimension of $\gamma$ is equal to $\operatorname {Min}(2,1+\kappa/8)$.

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Random walk reflected off of infinity, with applications to uniform spanning forests and supercritical Liouville quantum gravity
math.PR 2025-06 conditional novelty 9.0 of 10

A random walk that reflects off the boundary at infinity yields new algorithmic constructions of the free uniform spanning forest and a conjectural embedding framework for supercritical Liouville quantum gravity.

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