Abstract
Let be a d-dimensional critical super-Brownian motion started from a Poisson random measure whose intensity is the Lebesgue measure. Denote by the radius of the largest empty ball centered at the origin of . In this work, we prove that for ,
where satisfies
for some depending only on d.
Acknowledgements
The second author’s research is supported in part by NSFC grants 61873325, 11831010 and Southern University of Science and Technology Start up found Y01286120. The first author thanks Hui He for introducing the work of Révész (2002), which planted the seed of the current paper. He also would like to thank Lina Ji and Jiawei Liu for useful discussions. Both authors are grateful to the three reviewers for a number of helpful suggestions. Especially, according to one anonymous reviewer’s advice, by using (Dawson, Iscoe and Perkins, 1989, Theorem 3.3 (a)), the manuscript has been simplified substantially.
Citation
Shuxiong Zhang. Jie Xiong. "A note on the empty balls of a critical super-Brownian motion." Bernoulli 30 (1) 72 - 87, February 2024. https://doi.org/10.3150/22-BEJ1564
