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}
}
  • E. Broman
  • Published 1 March 2018
  • Mathematics
  • arXiv: Probability
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… 
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