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 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.
Cite
@article{arxiv.1912.06855,
title = {Planar maps and random partitions},
author = {Jérémie Bouttier},
journal= {arXiv preprint arXiv:1912.06855},
year = {2019}
}
Comments
Habilitation thesis, written in English except an introduction in French, 107 pages, many figures. Pages numbers differ from the printed copies given at the defence on 2 December 2019