On the Sobolev removability of the graph of one-dimensional Brownian motion
Suppose that B is a one-dimensional Brownian motion, and let Γ={(t,Bt):t∈[0,1]} be the graph of B|[0,1]. We characterize the Sobolev removability properties of Γ by showing that Γ is almost surely not W1,p-removable for all p∈[1,∞) but is almost surely W1,∞-removable.
Authors
- Jason Miller (ORCID: https://orcid.org/0000-0002-6912-2925)
- Cillian Doherty
Institutions
- University of Cambridge (GB)
- Institute of Mathematical Statistics (US)
Publication Details
- Journal
- The Annals of Probability
- Published
- 2026-06-30
- DOI
- https://doi.org/10.1214/25-aop1802
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00