Pattern occurrences in random planar maps

2018/01/30 by Michael Drmota, Benedikt Stufler, Drmota, Michael +1
Mathematics · #05C80 #60C05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #math.CO #math.PR #msc:05C80 #msc:60C05

paper · pdf · doi:10.48550/arxiv.1801.10007

arxiv created 2019/05/17 · arxiv updated 2019/05/20

Abstract

We consider planar maps adjusted with a (regular critical) Boltzmann distribution and show that the expected number of pattern occurrences of a given map is asymptotically linear when the number n of edges goes to infinity. The main ingredient for the proof is an extension of a formula by Liskovets (1999).

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