Gibbs Properties of the Bernoulli Field on Inhomogeneous Trees under the Removal of Isolated Sites

Florian Henning, Christof Külske (Corresponding author), Niklas Schubert

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We consider the i.i.d. Bernoulli field $\mu_p$ with occupation density
$p\in (0,1)$ on a possibly non-regular countably infinite tree with bounded degrees.
For large p, we show that the quasilocal Gibbs property, i.e. compatibility with
a suitable quasilocal specification, is lost under the deterministic transformation
which removes all isolated ones and replaces them by zeros, while a quasilocal
specification does exist at small p.
Our results provide an example for an independent field in a spatially non-homogeneous
setup which loses the quasilocal Gibbs property under a local
deterministic transformation.
Original languageEnglish
Pages (from-to)641-659
Number of pages19
JournalMarkov Processes and Related Fields
Issue number5
Publication statusPublished - 2023

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