Gibbs Properties of the Bernoulli Field on Inhomogeneous Trees under the Removal of Isolated Sites
Florian Henning, Christof Kuelske, Niklas Schubert
2023, v.29, Issue 5, 641-659
ABSTRACT
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.
doi:10.61102/1024-2953-mprf.2023.29.5.002
Keywords: Bernoulli field; non-regular tree; transformed measure; Gibbs property; quasilocality; cutset
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