A Strong Central Limit Theorem for a Class of Random Surfaces View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2014-01

AUTHORS

Joseph G. Conlon, Thomas Spencer

ABSTRACT

This paper is concerned with d = 2 dimensional lattice field models with action V(∇ϕ(·)), where V:Rd→R is a uniformly convex function. The fluctuations of the variable ϕ(0)-ϕ(x) are studied for large |x| via the generating function given by g(x,μ)=ln〈eμ(ϕ(0)-ϕ(x))〉A. In two dimensions g′′(x,μ)=∂2g(x,μ)/∂μ2 is proportional to ln|x|. The main result of this paper is a bound on g′′′(x,μ)=∂3g(x,μ)/∂μ3 which is uniform in |x| for a class of convex V. The proof uses integration by parts following Helffer–Sjöstrand and Witten, and relies on estimates of singular integral operators on weighted Hilbert spaces. More... »

PAGES

1-15

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-013-1843-6

DOI

http://dx.doi.org/10.1007/s00220-013-1843-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1005144616


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