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arXiv · 1912.06855

Planar maps and random partitions

Jérémie Bouttier
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Abstract

This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general map-mobile bijection, we compute the three-point function of quadrangulations, before discussing the connection with continued fractions. Chapter 2 presents the slice decomposition, a unified bijective approach that applies notably to irreducible maps. Chapter 3 concerns the $O(n)$ loop model on planar maps: by a combinatorial decomposition, we obtain the phase diagram before studying loop nesting statistics. Chapter 4 deals with random partitions and Schur processes, from steep domino tilings to fermionic systems.

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Jérémie Bouttier. 2019-12-14. Planar maps and random partitions. https://arxiv.org/abs/1912.06855

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