Asymptotic normality of pattern occurrences in random maps

2024/06/08 by Michael Drmota, Drmota, Michael, Eva‐Maria Hainzl +3
Mathematics · #05A16 05C10 05C80 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2406.05501

openalex publication_date 2024/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The purpose of this paper is to study the limiting distribution of special \it additive functionals on random planar maps, namely the number of occurrences of a given \it pattern. The main result is a central limit theorem for these pattern counts in the case of pattern with a simple boundary. The proof relies on a combination of analytic and combinatorial methods together with a moment method due to Gao and Wormald~\citeGaoWormald. It is an important issue to handle the overlap structure of two pattern which is the main difficulty in the proof.

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