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2018 How fast planar maps get swallowed by a peeling process
Nicolas Curien, Cyril Marzouk
Electron. Commun. Probab. 23: 1-11 (2018). DOI: 10.1214/18-ECP123

Abstract

The peeling process is an algorithmic procedure that discovers a random planar map step by step. In generic cases such as the UIPT or the UIPQ, it is known [15] that any peeling process will eventually discover the whole map. In this paper we study the probability that the origin is not swallowed by the peeling process until time $n$ and show it decays at least as $n^{-2c/3}$ where \[ c \approx 0.1283123514178324542367448657387285493314266204833984375... \] is defined via an integral equation derived using the Lamperti representation of the spectrally negative $3/2$-stable Lévy process conditioned to remain positive [12] which appears as a scaling limit for the perimeter process. As an application we sharpen the upper bound of the sub-diffusivity exponent for random walk of [4].

Citation

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Nicolas Curien. Cyril Marzouk. "How fast planar maps get swallowed by a peeling process." Electron. Commun. Probab. 23 1 - 11, 2018. https://doi.org/10.1214/18-ECP123

Information

Received: 12 January 2018; Accepted: 28 February 2018; Published: 2018
First available in Project Euclid: 7 March 2018

zbMATH: 1390.05214
MathSciNet: MR3779815
Digital Object Identifier: 10.1214/18-ECP123

Subjects:
Primary: 05C80, 05C81, 60G18

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