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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...

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Published in: The Annals of Applied Probability
ISSN: 1050-5164
Published: Institute of Mathematical Statistics 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa66126
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first_indexed 2024-06-27T11:57:14Z
last_indexed 2024-06-27T11:57:14Z
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spelling v2 66126 2024-04-22 Reconstruction of a multidimensional scenery with a branching random walk 1dc03e031f2f77c7df92f554c2043b0a Angelica Pachon Angelica Pachon true false 2024-04-22 MACS 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. Journal Article The Annals of Applied Probability 27 2 Institute of Mathematical Statistics 1050-5164 1 4 2017 2017-04-01 10.1214/16-aap1183 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2024-06-27T12:57:15.0260218 2024-04-22T15:24:49.6591258 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Heinrich Matzinger 1 Angelica Pachon 2 Serguei Popov 3
title Reconstruction of a multidimensional scenery with a branching random walk
spellingShingle Reconstruction of a multidimensional scenery with a branching random walk
Angelica Pachon
title_short Reconstruction of a multidimensional scenery with a branching random walk
title_full Reconstruction of a multidimensional scenery with a branching random walk
title_fullStr Reconstruction of a multidimensional scenery with a branching random walk
title_full_unstemmed Reconstruction of a multidimensional scenery with a branching random walk
title_sort Reconstruction of a multidimensional scenery with a branching random walk
author_id_str_mv 1dc03e031f2f77c7df92f554c2043b0a
author_id_fullname_str_mv 1dc03e031f2f77c7df92f554c2043b0a_***_Angelica Pachon
author Angelica Pachon
author2 Heinrich Matzinger
Angelica Pachon
Serguei Popov
format Journal article
container_title The Annals of Applied Probability
container_volume 27
container_issue 2
publishDate 2017
institution Swansea University
issn 1050-5164
doi_str_mv 10.1214/16-aap1183
publisher Institute of Mathematical Statistics
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 0
active_str 0
description 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.
published_date 2017-04-01T12:57:14Z
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score 11.013686

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