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The range of a self-similar additive gamma process is a scale invariant Poisson point process
Probability| Speaker: | Zhiyi You, UC Berkeley |
| Related Webpage: | https://statistics.berkeley.edu/people/zhiyi-you |
| Location: | Zoom |
| Start time: | Wed, Feb 9 2022, 1:10PM |
It is known as the scale invariant Poisson spacings theorem that the spacings between consecutive points of a scale invariant Poisson point process are the points of another scale invariant Poisson point process with the same intensity. This result arises in various contexts, including extremal processes and random permutations. In this talk, we place this result in a broader context of self-similar additive processes by giving its hold-jump description. The range of such process with gamma distributed marginals is proved to be a scale invariant Poisson point process, and then the scale invariant Poisson spacing theorem follows.