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  "body": "\n## Summary\n\nThe Schramm–Loewner evolution with parameter $\\kappa \u003e 0$, written $\\mathrm{SLE}_\\kappa$, is a random curve in a planar domain.\nIt is obtained from the [[Loewner differential equation|51G4QJZ345]] driven by a multiple of a Brownian motion.\nOded Schramm introduced it in 2000 as the candidate scaling limit of interfaces in planar models of statistical physics that are conformally invariant.\nIt is characterised by conformal invariance together with a domain Markov property, and the single parameter $\\kappa$ governs the shape of the curve.\n\n## Explanations\n\n### L1 human\n\nMany random paths on a fine lattice, such as the boundary of a cluster in critical percolation, look the same at every scale.\nIn the limit, they are unchanged by conformal maps.\nSchramm found that any such limiting random curve must be described by the Loewner equation with a driving function $\\sqrt{\\kappa}\\, B_t$, where $B_t$ is a Brownian motion.\nSmall $\\kappa$ gives curves that are nearly straight, and larger $\\kappa$ gives curves that wiggle more, touch themselves, and for $\\kappa \\ge 8$ fill the whole domain.\nFor example $\\kappa = 6$ describes the limit of percolation interfaces on the triangular lattice.\n",
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