A phase transition in block-weighted random maps

Autor:	Fleurat, William, Salvy, Zéphyr
Rok vydání:	2023
Předmět:	Mathematics - Probability Mathematics - Combinatorics 05C12 05C80 60D05 60F17 68R05 82B41
Druh dokumentu:	Working Paper
Popis:	We consider the model of random planar maps of size $n$ biased by a weight $u>0$ per $2$-connected block, and the closely related model of random planar quadrangulations of size $n$ biased by a weight $u>0$ per simple component. We exhibit a phase transition at the critical value $u_C=9/5$. If $u u_C$, the largest block is of size $\Theta(\log(n))$, the scaling order for distances is $n^{1/2}$, and the scaling limit is the Brownian tree. Finally, for $u=u_C$, the largest block is of size $\Theta(n^{2/3})$, the scaling order for distances is $n^{1/3}$, and the scaling limit is the stable tree of parameter $3/2$. Comment: 71 pages, 24 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.01723 Zobrazit plný text záznamu View this record from Arxiv