Contour lines of the two-dimensional discrete Gaussian free field

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dc.creatorSchramm, Oded
dc.creatorSheffield, Scott
dc.date2006-05-12
dc.date2008-04-24
dc.date.accessioned2026-07-07T09:34:32Z
dc.date.available2026-07-07T09:34:32Z
dc.descriptionWe prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant lambda > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain -- with boundary values -lambda on one boundary arc and lambda on the complementary arc -- the zero level line of h joining the endpoints of these arcs converges to SLE(4) as the domain grows larger. If instead the boundary values are -a < 0 on the first arc and b > 0 on the complementary arc, then the convergence is to SLE(4;a/lambda-1,b/lambda-1), a variant of SLE(4).
dc.description132 pages; minor revision
dc.identifierhttps://arxiv.org/abs/math/0605337
dc.identifierhttp://arxiv.org/abs/math/0605337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159523
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectComplex Variables
dc.titleContour lines of the two-dimensional discrete Gaussian free field
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