# The existence phase transition for scale invariant Poisson random fractal models

@article{Broman2018TheEP, title={The existence phase transition for scale invariant Poisson random fractal models}, author={Erik I. Broman}, journal={arXiv: Probability}, year={2018} }

In this paper we study the existence phase transition of scale invariant random fractal models. We determine the exact value of the critical point of this phase transition for all models satisfying two weak assumptions. In addition, we show that for a large subclass, the fractal model is in the empty phase at the critical point. This subclass of models includes the scale invariant Poisson Boolean model and the Brownian loop soup. In contrast to earlier results in the literature, we do not need…

## One Citation

The fractal cylinder process: Existence and connectivity phase transitions

- MathematicsThe Annals of Applied Probability
- 2021

We consider a semi-scale invariant version of the Poisson cylinder model which in a natural way induces a random fractal set. We show that this random fractal exhibits an existence phase transition…

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