Publications and Preprints

Criticality and covered area fraction in confetti percolation
Partha Pratim Ghosh and Rahul Roy
Using the randomized algorithm method developed by Duminil-Copin, Raoufi, Tassion (2016, 2017) we exhibit sharp phase transition for the confetti percolation model. This provides an alternate proof that the critical parameter for percolation in this model is $1/2$ when the underlying shapes for the distinct colours arise from the same distribution. This extends the work of Hirsch (2015) and M\"{u}ller (2016). In addition we study the covered area fraction for this model, which is akin to the covered volume fraction in continuum percolation. This study allows us to calculate exact critical parameter for percolation when the underlying shapes for different colours may be of different sizes subject to a certain `transitivity condition'.

isid/ms/2018/04 [fulltext]

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