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

Full text not available from this repository.

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.

[error in script] [error in script]

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

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item