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Type: Artigo
Title: Reconstruction of a multidimensional scenery with a branching random walk
Author: Matzinger, Heinrich
Pachon, Angelica
Popov, Serguei
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 Lowe 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.
Subject: Passeios aleatórios (Matemática)
Processo estocástico
Random walks (Mathematics)
Stochastic processes
Country: Estados Unidos
Editor: Institute of Mathematical Statistics
Rights: aberto
Identifier DOI: 10.1214/16-AAP1183
Date Issue: 2017
Appears in Collections:IMECC - Artigos e Outros Documentos

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