Asymptotic normality of pattern occurrences in random maps
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916280190107648 |
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| author | Drmota, Michael Hainzl, Eva-Maria Wormald, Nick |
| author_facet | Drmota, Michael Hainzl, Eva-Maria Wormald, Nick |
| contents | 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~\cite{GaoWormald}. It is an important issue to handle the overlap structure of two pattern which is the main difficulty in the proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_05501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic normality of pattern occurrences in random maps Drmota, Michael Hainzl, Eva-Maria Wormald, Nick Combinatorics Probability 05A16 05C10 05C80 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~\cite{GaoWormald}. It is an important issue to handle the overlap structure of two pattern which is the main difficulty in the proof. |
| title | Asymptotic normality of pattern occurrences in random maps |
| topic | Combinatorics Probability 05A16 05C10 05C80 |
| url | https://arxiv.org/abs/2406.05501 |