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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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Contributor : Jérémie Bouttier Connect in order to contact the contributor
Submitted on : Wednesday, December 18, 2019 - 10:09:52 AM
Last modification on : Sunday, June 26, 2022 - 2:45:01 AM
Long-term archiving on: : Thursday, March 19, 2020 - 4:07:14 PM


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  • HAL Id : tel-02417269, version 1


Jérémie Bouttier. Planar maps and random partitions. Mathematical Physics [math-ph]. Université Paris XI, 2019. ⟨tel-02417269⟩



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