A Strong Central Limit Theorem for a Class of Random Surfaces
Abstract
This paper is concerned with d = 2 dimensional lattice field models with action , where is a uniformly convex function. The fluctuations of the variable are studied for large  x via the generating function given by . In two dimensions is proportional to . The main result of this paper is a bound on which is uniform in for a class of convex V. The proof uses integration by parts following HelfferSjöstrand and Witten, and relies on estimates of singular integral operators on weighted Hilbert spaces.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 January 2014
 DOI:
 10.1007/s0022001318436
 Bibcode:
 2014CMaPh.325....1C