Scenery reconstruction with branching random walk
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 1744-2508Full text not available from this repository.
Official URL: http://dx.doi.org/10.1080/17442508.2010.544973
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.|
|Page Range:||pp. 107-116|
|References:|| K.B. Athreya and P.E. Ney, Branching Processes, Springer, New York, 1972.  G. Grimmett, Percolation, Springer-Verlag, New York, 1989.  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.  H. Kesten, The critical probability of bond percolation on the square lattice equals 1/2, Comm. Math. Phys. 74 (1980), pp. 41–59.  G. Lawler, Intersections of Random Walks, Birkha¨user, Boston, MA, 1991.  M. Lo¨we and H. Matzinger, Scenery reconstruction in two dimensions with many colors, Ann. Appl. Probab. 12 (2002), pp. 1322–1347.  H. Matzinger, Reconstructing a 2-color scenery by observing it along a simple random walk path, Ann. Appl. Probab. 15 (2005), pp. 778–819.  H. Matzinger and S.W.W. Rolles, Reconstructing a piece of scenery with polynomially many observations, Stoch. Process. Appl. 107 (2002), pp. 289–300.  K. Ulrich, Ergodic Theorems, Walter de Gruyter, Berlin/New York, 1985.  J.C. Wierman, Substitution method critical probability for the square lattice site percolation model, Combin. Prob. Comput. 4 (1995), pp. 181–188.|
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