CORE
🇺🇦Â
 make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
Properties of the gradient squared of the discrete Gaussian free field
Authors
Alessandra Cipriani
Rajat S. Hazra
Alan Rapoport
Wioletta M. Ruszel
Publication date
19 July 2022
Publisher
View
on
arXiv
Abstract
In this paper we study the properties of the centered (norm of the) gradient squared of the discrete Gaussian free field in
U
ϵ
=
U
/
ϵ
∩
Z
d
U_{\epsilon}=U/\epsilon\cap \mathbb{Z}^d
U
ϵ
​
=
U
/
ϵ
∩
Z
d
,
U
⊂
R
d
U\subset \mathbb{R}^d
U
⊂
R
d
and
d
≥
2
d\geq 2
d
≥
2
. The covariance structure of the field is a function of the transfer current matrix and this relates the model to a class of systems (e.g. height-one field of the Abelian sandpile model or pattern fields in dimer models) that have a Gaussian limit due to the rapid decay of the transfer current. Indeed, we prove that the properly rescaled field converges to white noise in an appropriate local Besov-H\"older space. Moreover, under a different rescaling, we determine the
k
k
k
-point correlation function and cumulants on
U
ϵ
U_{\epsilon}
U
ϵ
​
and in the continuum limit as
ϵ
→
0
\epsilon\to 0
ϵ
→
0
. This result is related to the analogue limit for the height-one field of the Abelian sandpile (\citet{durre}), with the same conformally covariant property in
d
=
2
d=2
d
=
2
.Comment: 28 page
Similar works
Full text
Available Versions
arXiv.org e-Print Archive
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:arXiv.org:2207.09401
Last time updated on 24/09/2022