The height gap of planar Brownian motion is $\frac{5}{\pi}$
| Autor: | Jego, Antoine, Lupu, Titus, Qian, Wei |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show that the occupation measure of planar Brownian motion exhibits a constant height gap of $5/\pi$ across its outer boundary. This property bears similarities with the celebrated results of Schramm--Sheffield [18] and Miller--Sheffield [12] concerning the height gap of the Gaussian free field across SLE$_4$/CLE$_4$ curves. Heuristically, our result can also be thought of as the $\theta \to 0^+$ limit of the height gap property of a field built out of a Brownian loop soup with subcritical intensity $\theta>0$, proved in our recent paper [3]. To obtain the explicit value of the height gap, we rely on the computation by Garban and Trujillo Ferreras [1] of the expected area of the domain delimited by the outer boundary of a Brownian bridge. Comment: 23 pages, 5 figures |
| Databáze: | arXiv |
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