On tessellations of random maps and the tg-recurrence
成果类型：
Article
署名作者：
Chapuy, Guillaume
署名单位：
Universite Paris Cite
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0865-6
发表日期：
2019
页码：
477-500
关键词：
摘要：
We study the masses of the two cells in a Voronoi tessellation of the Brownian surface of genus g0 centered on two uniform random points. Making use of classical bijections and asymptotic estimates for maps of fixed genus, we relate the second moment of these random variables to the Painleve-I equation satisfied by the double scaling limit of the one-matrix model, or equivalently to the tg-recurrence satisfied by the constants tg driving the asymptotic number of maps of genus g0. This raises the question of giving an independent probabilistic or combinatorial derivation of this second moment, which would then lead to new proof of the tg-recurrence. More generally we conjecture that for any g0 and k2, the masses of the cells in a Voronoi tessellation of the genus-g Brownian surface by k uniform points follows a Dirichlet(1,1,...,1) distribution.
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