2018/03/31 by Partha Pratim Ghosh, R. Roy, Rahul Roy · 1 citation
Chemistry · Mathematics · #Chemistry #Combinatorics #Criticality #Fraction (chemistry) #Geometry #Mathematical Dynamics and Fractals #Mathematics #Nuclear physics #Percolation (cognitive psychology) #Percolation theory #Percolation threshold #Physics #Random Matrices and Applications #Self-organized criticality #Statistical physics #Stochastic processes and statistical mechanics #Topology (electrical circuits) #Voronoi diagram #math.PR #msc:60K35
paper · pdf · doi:10.1007/s10955-021-02859-2
published as Journal of Statistical Physics, 186(1): Paper No. 20 (2022), 1-26 · 34 pages
openalex publication_date 2021/12/31 · arxiv created 2022/01/02 · arxiv updated 2022/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using the randomized algorithm method developed by Duminil-Copin, Raoufi and Tassion (2019b), we exhibit sharp phase transition for the confetti percolation model. This provides an alternate proof, than that of Ahlberg, Tassion and Texeira (2018), for the critical parameter for percolation in this model to be 1/2 when the radius of the underlying shapes for the distinct colours arise from the same distribution. In addition, we study the covered area fraction for this model, which is akin to the covered volume fraction in continuum percolation. Modulo a certain `transitivity condition', this study allows us to calculate exact critical parameter for percolation when the underlying shapes for different colours may be of different sizes. Similar results are also obtained for the Poisson Voronoi percolation model when different coloured points have different growth speeds.