Two-Dimensional Brownian Random Interlacements

Author(s)

Comets, Francis ^{[1, 2]} ; Popov, Serguei ^[3]

Affiliation

^[1] Univ Paris Diderot, Math, 8 Pl Aurelie Nemours, F-75013 Paris - France

^[2] SU, UPD, CNRS, LPSM, UMR 8001, Paris - France

^[3] Univ Campinas UNICAMP, Inst Math Stat & Sci Computat, Dept Stat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: POTENTIAL ANALYSIS; v. 53, n. 2, p. 727-771, AUG 2020.
• Web of Science Citations: 0

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 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. (AU)

• FAPESP's process: 17/02022-2 - Random interlacement models
• Grantee: Serguei Popov
• Support Opportunities: Regular Research Grants