Work

Asymptotic normality of pattern occurrences in random maps

Year: 2025

Type: article

Abstract: The purpose of this paper is to study the limiting distribution of special additive functionals on random planar maps, namely the number of occurrences of a given pattern. The main result is a central limit theorem for these pattern counts in the case of patterns 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 [Probab. Theory Relat. Fields 130 (2004), 368–376]. It is an important issue to handle the overlap structure of two patterns which is the main difficulty in the proof.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70149

Authors: Michael Drmota, Eva‐Maria Hainzl, Nick Wormald

Institutions: TU Wien, Monash University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Austrian Science Fund

Awards: G1507904531, Infinite Singular Systems and Random Discrete Objects