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This article is cited in 1 scientific paper (total in 1 paper)
2–3 Paths in a Lattice Graph: Random Walks
I. M. Erusalimskyi Southern Federal University, Rostov-on-Don
Abstract:
A lattice graph with 2–3 reachability constraints is considered. The graph's vertices are the points with integer nonnegative coordinates in the plane. Each vertex has two outgoing edges, one entering its immediate right neighbor and the other entering its immediate upper neighbor. The admissible paths for 2–3 reachability are those in which the numbers of edges in all but the last inclusion-maximal straight-line segments are divisible by $2$ for horizontal segments and by $3$ for vertical segments. A formula for the number of 2–3 paths from a vertex to a vertex is obtained. A random walk process on the 2–3 paths in the lattice graph is considered. It is proved that this process can locally be reduced to a Markov process on subgraphs determined by the type of the initial vertex. Formulas for the probabilities of vertex-to-vertex transitions along 2–3 paths are obtained.
Keywords:
digraph, lattice graph, random walk, transition probability, vertex reachability.
DOI:
https://doi.org/10.4213/mzm12111
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English version:
Mathematical Notes, 2018, 104:3, 395–403
Bibliographic databases:
UDC:
519.1 Received: 02.12.2017
Citation:
I. M. Erusalimskyi, “2–3 Paths in a Lattice Graph: Random Walks”, Mat. Zametki, 104:3 (2018), 396–406; Math. Notes, 104:3 (2018), 395–403
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/mz12111https://doi.org/10.4213/mzm12111 http://mi.mathnet.ru/eng/mz/v104/i3/p396
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This publication is cited in the following articles:
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I. M. Erusalimskiy, K. L. Pevneva, “Graphs with table constraints on reachability”, Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 1479, IOP Publishing Ltd, 2020, 012028
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