Contour lines of the two-dimensional discrete Gaussian free field

Oded Schramm Theory Group of Microsoft Research, One Microsoft Way Scott Sheffield Courant Institute, New York University

TBD mathscidoc:1701.332001

Acta Mathematica, 202, (1), 21-137, 2006.10
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).
No keywords uploaded!
[ Download ] [ 2017-01-08 20:33:52 uploaded by actaadmin ] [ 56 downloads ] [ 0 comments ]
@inproceedings{oded2006contour,
  title={Contour lines of the two-dimensional discrete Gaussian free field},
  author={Oded Schramm, and Scott Sheffield},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203352840250710},
  booktitle={Acta Mathematica},
  volume={202},
  number={1},
  pages={21-137},
  year={2006},
}
Oded Schramm, and Scott Sheffield. Contour lines of the two-dimensional discrete Gaussian free field. 2006. Vol. 202. In Acta Mathematica. pp.21-137. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203352840250710.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved