MIT Combinatorics Seminar
A random tiling model for two dimensional electrostatics II: arbitrary charge distributions under periodic boundary conditions
Mihai Ciucu
(Georgia Tech)
http://www.math.gatech.edu/~ciucu/
Friday, December 03, 2004
4:15 pm Room 2338
ABSTRACT

In a talk given in this seminar last spring we defined the correlation of holes
on the triangular lattice by including them in large hexagons that were grown
to infinity so that the holes remained near the center. We showed that if the
holes are distributed symetrically about a straight line, then for large
distances between the holes the correlation behaves like the electrostatic
energy of a two dimensional system of charges corresponding to the holes. Since
the dimer statistics is significantly distorted almost everywhere inside
hexagonal regions, it arises as a desirable goal to define the correlation of
holes in an alternate way, via regions that don't distort dimer statistics, and
analyze its asymptotic behavior. In the present talk we define such a
correlation and prove that it also reduces to electrostatics in the scaling
limit. Our proof applies to general, not necessarily symmetric distributions of
the holes.


