Year: 2026
Type: preprint
Abstract: Let $\mathcal{C}_\varepsilon$ denote the time it takes a Brownian motion to come within distance $\varepsilon$ of every point in the two dimensional torus $\mathbb{T}^2$ of unit area. We prove that for an explicit non-random centering $m_\varepsilon$, the variables $\{\sqrt{\mathcal{C}_{\varepsilon}} - m_\varepsilon \}$ converge in distribution as $\varepsilon \to 0$, to a randomly shifted Gumbel law.
Source: arXiv (Cornell University)
Authors: Dembo, Amir, Rosen, Jay, Zeitouni, Ofer
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7220387602