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April 2017 Reconstruction of a multidimensional scenery with a branching random walk
Heinrich Matzinger, Angelica Pachon, Serguei Popov
Ann. Appl. Probab. 27(2): 651-685 (April 2017). DOI: 10.1214/16-AAP1183

Abstract

We consider a $d$-dimensional scenery seen along a simple symmetric branching random walk, where at each time each particle gives the color record it observes. We show that up to equivalence the scenery can be reconstructed a.s. from the color record of all particles. To do so, we assume that the scenery has at least $2d+1$ colors which are i.i.d. with uniform probability. This is an improvement in comparison to Popov and Pachon [Stochastics 83 (2011) 107–116], where at each time the particles needed to see a window around their current position, and in Löwe and Matzinger [Ann. Appl. Probab. 12 (2002) 1322–1347], where the reconstruction is done for $d=2$ with a single particle instead of a branching random walk, but millions of colors are necessary.

Citation

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Heinrich Matzinger. Angelica Pachon. Serguei Popov. "Reconstruction of a multidimensional scenery with a branching random walk." Ann. Appl. Probab. 27 (2) 651 - 685, April 2017. https://doi.org/10.1214/16-AAP1183

Information

Received: 1 March 2014; Revised: 1 June 2015; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1370.60146
MathSciNet: MR3655850
Digital Object Identifier: 10.1214/16-AAP1183

Subjects:
Primary: 60J05, 60J80

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 2 • April 2017
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