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On the triviality of the shocked map

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorFREDES, Luis
hal.structure.identifierDepartamento de Ingeniería Matemática [Santiago] [DIM]
dc.contributor.authorSEPÚLVEDA, Avelio
dc.date.accessioned2024-04-04T02:33:17Z
dc.date.available2024-04-04T02:33:17Z
dc.date.created2023-09-11
dc.date.issued2023-09-11
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190463
dc.description.abstractEnThe (non-spanning) tree-decorated quadrangulation is a random pair formed by a quadrangulation and a subtree chosen uniformly over the set of pairs with prescribed size. In this paper we study the tree-decorated quadrangulation in the critical regime: when the number of faces of the map, $f$, is proportional to the square of the size of the tree. We show that with high probability in this regime, the diameter of the tree is between $o(f^{1/4})$ and $f^{1/4}/\log^\alpha(f)$, for $\alpha >1$. Thus after scaling the distances by $f^{-1/4}$, the critical tree-decorated quadrangulation converges to a Brownian disk where the boundary has been identified to a point. These results imply the triviality of the shocked map: the metric space generated by gluing a Brownian disk with a continuous random tree.
dc.language.isoen
dc.title.enOn the triviality of the shocked map
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halMathématiques [math]/Combinatoire [math.CO]
dc.identifier.arxiv2309.05540
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04205374
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04205374v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-09-11&rft.au=FREDES,%20Luis&SEP%C3%9ALVEDA,%20Avelio&rft.genre=preprint


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