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This article is cited in 2 scientific papers (total in 2 papers)
Theory of probability and Mathematical statistics
Monotonicity of random walks' states on finite grids
A. O. Zadorozhnuyk EPAM Systems, 1 Akademika Kuprevica Street, 1 building, Minsk 220141, Belarus
Abstract:
In this paper two ways to order the nodes of a graph with respect to an arbitrary node are considered, both connected to random walks on the graph. The first one is the order according to probabilities of states of a random walk of fixed length started in that arbitrary node. The walks considered here are lazy walks – instead of making a step they are allowed to stay in the same node. A class of graphs, where such order the corresponds to the weak order by geodesic distances, was found. Square and toric $n$-dimensional grids are shown to be instances of this class. The second way of ordering is resistance distance to a fixed node. For another class of graphs, a pair of vertices with maximal resistance distance between them is established. Grids are again shown to be an example of graphs belonging to this class.
Keywords:
random walks; resistance distance; grids.
Received: 12.01.2022 Revised: 13.01.2022 Accepted: 14.02.2022
Citation:
A. O. Zadorozhnuyk, “Monotonicity of random walks' states on finite grids”, Journal of the Belarusian State University. Mathematics and Informatics, 1 (2022), 38–45
Linking options:
https://www.mathnet.ru/eng/bgumi176 https://www.mathnet.ru/eng/bgumi/v1/p38
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Abstract page: | 72 | Full-text PDF : | 52 | References: | 16 |
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