Scaling limit for a class of gradient fields with non-convex potentials

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12510%2F11%3A43870190" target="_blank" >RIV/60076658:12510/11:43870190 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1214/10-AOP548" target="_blank" >http://dx.doi.org/10.1214/10-AOP548</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/10-AOP548" target="_blank" >10.1214/10-AOP548</a>

Result language
angličtina
Original language name
Scaling limit for a class of gradient fields with non-convex potentials
Original language description
We consider gradient fields (phi(x) : x is an element of Z(d)) whose law takes the Gibbs-Boltzmann form Z(-1) exp{-Sigma({ x,y }) V(phi(y) - phi(x))}, where the sum runs over nearest neighbors. We assume that the potential V admits the representation V(eta) := -log integral rho(dk)exp[-1/2 kappa eta(2)], where rho is a positive measure with compact support in (0, infinity). Hence, the potential V is symmetric, but nonconvex in general. While for strictly convex V's, the translation-invariant, ergodic gradient Gibbs measures are completely characterized by their tilt, a nonconvex potential as above may lead to several ergodic gradient Gibbs measures with zero tilt. Still, every ergodic, zero-tilt gradient Gibbs measure for the potential V above scales to a Gaussian free field.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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