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Scenery reconstruction with branching random walk
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Popov, Serguei and Pachon, Angelica. (2011) Scenery reconstruction with branching random walk. Stochastics An International Journal of Probability and Stochastic Processes, Volume 83 (Number 2). pp. 107-116. ISSN 1744-2508
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Official URL: http://dx.doi.org/10.1080/17442508.2010.544973
Abstract
We study the problem of scenery reconstruction in arbitrary dimension using observations registered in boxes of size k (for k fixed), seen along a branching random walk. We prove that, using a large enough k for almost all the realizations of the branching random walk, almost all sceneries can be reconstructed up to equivalence.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Library of Congress Subject Headings (LCSH): | Random walks (Mathematics), Branching processes |
| Journal or Publication Title: | Stochastics An International Journal of Probability and Stochastic Processes |
| Publisher: | Taylor & Francis Ltd. |
| ISSN: | 1744-2508 |
| Date: | 2011 |
| Volume: | Volume 83 |
| Number: | Number 2 |
| Page Range: | pp. 107-116 |
| Identification Number: | 10.1080/17442508.2010.544973 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| References: | [1] K.B. Athreya and P.E. Ney, Branching Processes, Springer, New York, 1972. [2] G. Grimmett, Percolation, Springer-Verlag, New York, 1989. [3] H. Kesten, Distinguishing and reconstructing sceneries from observations along random walk paths, in Microsurveys in Discrete Probability (Princeton, NJ, 1997), American Mathematical Society, Providence, RI, 1998, pp. 75–83. [4] H. Kesten, The critical probability of bond percolation on the square lattice equals 1/2, Comm. Math. Phys. 74 (1980), pp. 41–59. [5] G. Lawler, Intersections of Random Walks, Birkha¨user, Boston, MA, 1991. [6] M. Lo¨we and H. Matzinger, Scenery reconstruction in two dimensions with many colors, Ann. Appl. Probab. 12 (2002), pp. 1322–1347. [7] H. Matzinger, Reconstructing a 2-color scenery by observing it along a simple random walk path, Ann. Appl. Probab. 15 (2005), pp. 778–819. [8] H. Matzinger and S.W.W. Rolles, Reconstructing a piece of scenery with polynomially many observations, Stoch. Process. Appl. 107 (2002), pp. 289–300. [9] K. Ulrich, Ergodic Theorems, Walter de Gruyter, Berlin/New York, 1985. [10] J.C. Wierman, Substitution method critical probability for the square lattice site percolation model, Combin. Prob. Comput. 4 (1995), pp. 181–188. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/34861 |
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