NDLI: Inhomogeneous Markov Approach to Percolation Theory Based Propagation in Random Media

Content Provider	IEEE Xplore Digital Library
Author	Bender, A. Rainsford, T.
Copyright Year	1963
Abstract	In recent years it has been shown that ray propagation in two-dimensional (2D) uniform random percolation lattices is well approximated by stochastic processes. Two of the probabilistic interpretations can be solved exactly but impose some additional restrictions on the ray dynamics: the 1999 model by G. Franceschetti demands that ray reflections inside the lattice are independent and identically distributed (IID); and the 2006 model by A. Martini assumes that for the analysis of vertical ray penetration reflections on vertical lattice cell faces can be neglected. In this paper we present a 2D generalization of the 1999 model that does not rely on the IID assumption. It is based on a set of coupled iteration formulas for right stochastic matrices that describe a time-inhomogeneous Markov process. Upon expanding the space of transition states, the iterative process can be recast in the projection of a time-homogeneous Markov chain. Thus the Perron-Frobenius theorem can be applied to analyze the stationary states of the process, which leads to a simple analytical expression for the probability of a ray ensemble reaching a specified lattice level after infinitely many reflections. We discuss different boundary conditions at the absorbing barriers of the ray propagation process and show that (1) by imposing the IID assumption, the 1999 model by G. Francescetti can be recovered; and (2) a one-dimensional reduction of the approach exactly leads to the 2006 model by A. Martini The presented stochastic approach provides a framework in which basic assumptions of probabilistic interpretations of percolation theory based ray propagation can be studied in some detail. It also allows for the consistent derivation of the stationary probability states which are needed to apply the approach to a wider range of phenomena such as internal-source ray propagation in both uniform and nonuniform random media.
Sponsorship	IEEE Antennas and Propagation Society
Starting Page	3271
Ending Page	3284
Page Count	14
File Size	1040259
File Format	PDF
ISSN	0018926X
Volume Number	56
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Random media Lattices Stochastic processes Solid modeling Reflection Markov processes Wireless communication Propagation losses Delay effects Australia urban areas Electromagnetic propagation in random media martingales mobile communication
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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