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May 2020 On the topological boundary of the range of super-Brownian motion
Jieliang Hong, Leonid Mytnik, Edwin Perkins
Ann. Probab. 48(3): 1168-1201 (May 2020). DOI: 10.1214/19-AOP1386

Abstract

We show that if $\partial\mathcal{R}$ is the boundary of the range of super-Brownian motion and dim denotes Hausdorff dimension, then with probability one, for any open set $U$, $U\cap\partial\mathcal{R}\neq\varnothing$ implies \[\operatorname{dim}(U\cap\partial\mathcal{R})=\begin{cases}4-2\sqrt{2}\approx1.17\quad\text{if }d=2,\\\frac{9-\sqrt{17}}{2}\approx2.44\quad\text{if }d=3.\end{cases}\] This improves recent results of the last two authors by working with the actual topological boundary, rather than the boundary of the zero set of the local time, and establishing a local result for the dimension.

Citation

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Jieliang Hong. Leonid Mytnik. Edwin Perkins. "On the topological boundary of the range of super-Brownian motion." Ann. Probab. 48 (3) 1168 - 1201, May 2020. https://doi.org/10.1214/19-AOP1386

Information

Received: 1 September 2018; Revised: 1 May 2019; Published: May 2020
First available in Project Euclid: 17 June 2020

zbMATH: 07226357
MathSciNet: MR4112711
Digital Object Identifier: 10.1214/19-AOP1386

Subjects:
Primary: 60G57, 60J68
Secondary: 35J75, 60H30, 60J80

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • May 2020
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