Journal article 19 views
Reconstruction of a multidimensional scenery with a branching random walk
Heinrich Matzinger,
Angelica Pachon,
Serguei Popov
The Annals of Applied Probability, Volume: 27, Issue: 2
Swansea University Author: Angelica Pachon
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DOI (Published version): 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 scen...
| Published in: | The Annals of Applied Probability |
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| ISSN: | 1050-5164 |
| Published: |
Institute of Mathematical Statistics
2017
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa66126 |
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| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
2 |