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arXiv · 1804.05967

Two-dimensional Brownian random interlacements

Francis Comets·Serguei Popov
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Abstract

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, Popov, Vachkovskaia, 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, Popov, Vachkovskaia, 2016; Comets, Popov, 2016], as well as the results specific to the continuous case.

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Francis Comets, Serguei Popov. 2019-04-16. Two-dimensional Brownian random interlacements. https://doi.org/10.1007/s11118-019-09786-8

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