Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites

Florian Henning; Christof Külske; Niklas Schubert

doi:10.61102/1024-2953-mprf.2023.29.5.002

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arXiv · 2304.03102

Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites

Florian Henning·Christof Külske·Niklas Schubert

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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.

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BibTeX RIS

Florian Henning, Christof Külske, Niklas Schubert. 2023-04-06. Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites. https://doi.org/10.61102/1024-2953-mprf.2023.29.5.002

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