Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909132884279296 |
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| author | Henning, Florian Külske, Christof Schubert, Niklas |
| author_facet | Henning, Florian Külske, Christof Schubert, Niklas |
| contents | We consider the i.i.d. Bernoulli field $μ_p$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_03102 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites Henning, Florian Külske, Christof Schubert, Niklas Probability Mathematical Physics 82B26 (primary), 60K35 (secondary) We consider the i.i.d. Bernoulli field $μ_p$ 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. |
| title | Gibbs Properties of the Bernoulli field on inhomogeneous trees under the removal of isolated sites |
| topic | Probability Mathematical Physics 82B26 (primary), 60K35 (secondary) |
| url | https://arxiv.org/abs/2304.03102 |