布朗球体中的蛇

摘要

布朗球体是一种随机度量空间，同胚于二维球面，它作为多种随机平面图普适的尺度极限而出现。布朗球体的直接构建是通过Cori-Vauquelin-Schaeffer（CVS）双射的连续类比实现的。CVS双射将标记树映射到平面图，而其连续版本则将带有布朗标记的Aldous连续随机树（即布朗蛇）映射到布朗球体。在本研究中，我们通过将布朗蛇构造为布朗球体的可测函数，描述了连续CVS双射的逆映射。在处理布朗球体的定向时，需要特别谨慎。

English

The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direct construction of the Brownian sphere is via a continuous analogue of the Cori--Vauquelin--Schaeffer (CVS) bijection. The CVS bijection maps labeled trees to planar maps, and the continuous version maps Aldous' continuum random tree with Brownian labels (the Brownian snake) to the Brownian sphere. In this work, we describe the inverse of the continuous CVS bijection, by constructing the Brownian snake as a measurable function of the Brownian sphere. Special care is needed to work with the orientation of the Brownian sphere.

布朗球体中的蛇

The snake in the Brownian sphere

摘要

Summary

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