Decorrelation of a class of Gibbs particle processes and asymptotic properties ofU-statistics

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10417609" target="_blank" >RIV/00216208:11320/20:10417609 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eCdJfdr5Nd" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eCdJfdr5Nd</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jpr.2020.51" target="_blank" >10.1017/jpr.2020.51</a>

Result language
angličtina
Original language name
Decorrelation of a class of Gibbs particle processes and asymptotic properties ofU-statistics
Original language description
We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation, we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of aU-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for suchU-statistics of the Gibbs particle process. A by-product of our approach is a new uniqueness result for Gibbs particle processes.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA19-04412S" target="_blank" >GA19-04412S: New approaches to modeling and statistics of random sets</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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