Contour lines of the two-dimensional discrete Gaussian free field |
| |
Authors: | Oded Schramm Scott Sheffield |
| |
Institution: | 1.Theory Group of Microsoft Research,One Microsoft Way,Redmond,USA;2.Courant Institute,New York University,New York,USA |
| |
Abstract: | We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there
is a constant λ > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain—with boundary values −λ on one boundary arc and
λ 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/λ - 1, b/λ - 1), a variant of SLE(4). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|