Open Access
2019 Shape theorem and surface fluctuation for Poisson cylinders
Marcelo Hilario, Xinyi Li, Petr Panov
Electron. J. Probab. 24: 1-16 (2019). DOI: 10.1214/19-EJP329


We prove a shape theorem for Poisson cylinders, and give a power-law bound on surface fluctuations. In particular, we show that for any $a \in (1/2, 1)$, conditioned on the origin being in the set of cylinders, if a point belongs to this set and has Euclidean norm below $R$, then this point lies at internal distance less than $R + O(R^{a})$ from the origin.


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Marcelo Hilario. Xinyi Li. Petr Panov. "Shape theorem and surface fluctuation for Poisson cylinders." Electron. J. Probab. 24 1 - 16, 2019.


Received: 27 July 2018; Accepted: 28 May 2019; Published: 2019
First available in Project Euclid: 28 June 2019

zbMATH: 07089006
MathSciNet: MR3978218
Digital Object Identifier: 10.1214/19-EJP329

Primary: 51F99 , 60F10 , 60K35 , 82B43

Keywords: Internal distance , Poisson cylinder model , shape theorem

Vol.24 • 2019
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