Random maps from Z2 to Z


Richard Kenyon

Université Paris-Sud

Harvard University

Thursday, November 15 , 2001


Talk at 4:30 p.m. in Science Center D

Tea at 4:00 p.m. in the Math Lounge


Abstract:   We study a particular family of random maps from Z2 to Z, arising from "lozenge tilings" of the plane. If we fix a finite domain U in Z2 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.


Home Web page:  Alexandru I. Suciu  Comments to: 
Created: October 31, 2001    URL: