The existence phase transition for scale invariant Poisson random fractal models
Journal article, 2020

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 some 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 to restrict our attention to random fractal models generated by open sets.

Poissonian random fractals

Phase transition


Erik Broman

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Annales de linstitut Henri Poincare (B) Probability and Statistics

0246-0203 (ISSN)

Vol. 56 1 715-733

Subject Categories

Other Physics Topics


Probability Theory and Statistics



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6/2/2020 1