On the topological boundary of the range of super-Brownian motion-extended version

2018/09/12 by Jieliang Hong, Hong, Jieliang, Leonid Mytnik +3
Mathematics · #35J75 (secondary) #60G57 (primary) 60H30 #60J68 #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1809.04238

openalex publication_date 2018/09/12 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

We show that if \partialR is the boundary of the range of super-Brownian motion and dim denotes Hausdorff dimension, then with probability one, for any open set U, \partialR∩ U≠∅ implies dim(U∩\partialR)=\begincases 4-2√2≈1.17amp; if d=2
(9-√(17))/(2)≈ 2.44amp; if d=3. \endcases This improves recent results of the last two authors (arxiv:1711.03486) 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.

Citations

• The dimension of the boundary of super-Brownian motion

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