We introduce the model of two-dimensional continuous random interlacements, which is constructed using the Brownian trajectories conditioned on not hitting a fixed set (usually, a disk). This model yields the local picture of Wiener sausage on the torus around a late point. As such, it can be seen as a continuous analogue of discrete two-dimensional random interlacements (Comets et al. Commun. Math. Phys. 343, 129–164, 2016). At the same time, one can view it as (restricted) Brownian loops through infinity. We establish a number of results analogous to these of Comets and Popov (Ann. Probab. 45, 4752–4785, 2017), Comets et al. (Commun. Math. Phys. 343, 129–164, 2016), as well as the results specific to the continuous case.

中文翻译：

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二维布朗随机交织

我们介绍了二维连续随机交织模型，该模型是使用布朗轨迹建立的，该布朗轨迹的条件是不击中固定集（通常是磁盘）。该模型可得出圆点附近维纳香肠的局部图片。因此，它可以被看作是离散二维随机interlacements的连续类似物（彗星等。COMMUN。数学式的PHY。343，129-164，2016）。同时，人们可以将其视为无限的布朗循环（受限）。我们建立了类似于这些彗星和波波夫（安。Probab。的多项成果45，4752-4785，2017），彗星等。（COMMUN。数学式的PHY。343，129-164，2016），以及结果特定于连续的情况。