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

Florian Henning, Christof Külske, Niklas Schubert

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 th…