Large-Deviation Analysis for Canonical Gibbs Measures
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10500657" target="_blank" >RIV/00216208:11320/25:10500657 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rglljUs3.C" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=rglljUs3.C</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10955-025-03451-8" target="_blank" >10.1007/s10955-025-03451-8</a>
Alternative languages
Result language
angličtina
Original language name
Large-Deviation Analysis for Canonical Gibbs Measures
Original language description
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of increasing windows. Our method relies on the traditional large-deviation result for local bounded functionals of Poisson point processes noting that the binomial point process is obtained from the Poisson point process by conditioning on the point number. Our main methodological contribution is the development of coupling constructions allowing us to handle delicate and unlikely pathological events. The presented results cover three types of Gibbs models - a model given by a bounded local interaction, a model given by a non-negative possibly unbounded increasing local interaction and the hard-core interaction model. The derived large deviation principle is formulated for the distributions of individual empirical fields driven by canonical Gibbs processes, with its special case being a large deviation principle for local bounded observables of the canonical Gibbs processes. We also consider unbounded non-negative increasing local observables, but the price for treating this more general case is that we only get large-deviation bounds for the tails of such observables. Our primary setting is the one with periodic boundary condition, however, we also discuss generalizations for different choices of the boundary condition.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Statistical Physics
ISSN
0022-4715
e-ISSN
1572-9613
Volume of the periodical
192
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
50
Pages from-to
71
UT code for WoS article
001485771700001
EID of the result in the Scopus database
2-s2.0-105004454947