The existence phase transition for scale invariant Poisson random\n fractal models

2018/03/01 by Erik I. Broman, Broman, Erik I.
Mathematics · Physics and Astronomy · #60K35 28A80 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1803.00258

openalex publication_date 2018/03/01 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence phase transition of scale invariant\nrandom fractal models. We determine the exact value of the critical point of\nthis phase transition for all models satisfying some weak assumptions. In\naddition, we show that for a large subclass, the fractal model is in the empty\nphase at the critical point. This subclass of models includes the scale\ninvariant Poisson Boolean model and the Brownian loop soup. In contrast to\nearlier results in the literature, we do not need to restrict our attention to\nrandom fractal models generated by open sets.\n

Related

• The fractal cylinder process: existence and connectivity phase transition
• Percolation of fat Poisson cylinders in hyperbolic space
• Anomalous Scaling and Fractal Dimensions
• Non-existence of several random fractals in the Brownian motion and the Brownian loop soup
• Discontinuity of the phase transition for the planar random-cluster and Potts models with q>4