Work

Zeros of the Brownian Sheet

Year: 2025

Type: article

Abstract: In this work, we firstly answer to a question raised by Khoshnevisan (Trans Am Math Soc 359:3125–3151, 2007) [Open Problem 4] by proving that almost surely there is no projection of big enough rank changing the Hausdorff dimension of the zeros of the Brownian sheet. Secondly, we prove that almost surely for every projection whose rank is not matching the aforementioned condition, the projection of the zero set is the entirety of the projective space.

Source: Journal of Theoretical Probability

DOI: 10.1007/s10959-024-01399-1

Authors: Keming Chen, Guillaume Woessner

Institution: École Polytechnique Fédérale de Lausanne

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: École Polytechnique Fédérale de Lausanne