RECONSTRUCTION OF A MULTIDIMENSIONAL SCENERY WITH A BRANCHING RANDOM WALK

• 成果类型: Article
• 署名作者: Matzinger, Heinrich; Pachon, Angelica; Popov, Serguei
• 署名单位: University System of Georgia; Georgia Institute of Technology; University of Turin; Universidade Estadual de Campinas
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1183
• 发表日期: 2017
• 页码: 651-685
• 关键词: path

摘要

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.