The existence phase transition for scale invariant Poisson random fractal models
Artikel i vetenskaplig tidskrift, 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

Författare

Erik Broman

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Annales de linstitut Henri Poincare (B) Probability and Statistics

0246-0203 (ISSN)

Vol. 56 1 715-733

Ämneskategorier

Annan fysik

Geofysik

Sannolikhetsteori och statistik

DOI

10.1214/19-AIHP978

Mer information

Senast uppdaterat

2020-06-02