Random maps from Z^{2} to Z |
Abstract: We study a particular family of random maps from Z^{2} to Z, arising from "lozenge tilings" of the plane. If we fix a finite domain U in Z^{2} and a set of boundary values for the map, what can be said about the typical behavior of the map in the interior of U? For the present model we will show how, for "nice" boundary values, the scaling limit (limit when the lattice spacing tends to zero) gives a simple conformally invariant random object, the "massless free field". We also discuss the conjecture that, for more general boundary values, the limiting object is still the massless free field for a nonstandard conformal structure arising from solving a certain Beltrami equation in U. |
Web page: Alexandru I. Suciu | Comments to: alexsuciu@neu.edu | |
Created: October 31, 2001 | URL: http://www.math.neu.edu/bhmn/kenyon.html |