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Habilitation à diriger des recherches

Planar maps and random partitions

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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https://tel.archives-ouvertes.fr/tel-02417269
Contributor : Jérémie Bouttier <>
Submitted on : Wednesday, December 18, 2019 - 10:09:52 AM
Last modification on : Monday, February 10, 2020 - 6:13:42 PM
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Jérémie Bouttier. Planar maps and random partitions. Mathematical Physics [math-ph]. Université Paris XI, 2019. ⟨tel-02417269⟩

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