Geodesic
Asymptotics of the Number of End Positions of a Random Walk on a Directed Hamiltonian Metric Graph
Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 560-576 Cet article a éte moissonné depuis la source Math-Net.Ru

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The asymptotics of the number of end positions of a random walk on an oriented Hamiltonian metric graph is obtained.
Keywords: counting function, directed graph, dynamical system
Mots-clés : Bernoulli–Barnes polynomial. 
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D. V. Pyatko; V. L. Chernyshev. Asymptotics of the Number of End Positions of a Random Walk on a Directed Hamiltonian Metric Graph. Matematičeskie zametki, Tome 113 (2023) no. 4, pp. 560-576. http://geodesic.mathdoc.fr/item/MZM_2023_113_4_a6/

[1] G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, Math. Surveys and Monographs, 186, AMS, Providence, RI, 2014 | MR

[2] L. Lovasz, “Random walks on graphs: a survey”, Combinatorics, Paul Erdos is Eighty (Keszthely, 1993), Bolyai Soc. Math. Stud., 2, Janos Bolyai Math. Soc., Budapest, 1996, 353–397 | MR

[3] V. L. Chernyshev, A. A. Tolchennikov, “Polynomial approximation for the number of all possible endpoints of a random walk on a metric graph”, TCDM 2018 2-nd IMA Conference on Theoretical and Computational Discrete Mathematics, Electron. Notes Discrete Math., 70, Elsevier, Amsterdam, 2018, 31–35 | DOI | MR | Zbl

[4] V. L. Chernyshev, A. A. Tolchennikov, “Correction to the leading term of asymptotics in the problem of counting the number of points moving on a metric tree”, Russ. J. Math. Phys., 24:3 (2017), 290–298 | DOI | MR

[5] V. L. Chernyshev, A. A. Tolchennikov, “The second term in the asymptotics for the number of points moving along a metric graph”, Regul. Chaotic Dyn., 22:8 (2017), 937–948 | DOI | MR

[6] V. L. Chernyshev, A. I. Shafarevich, “Statistics of Gaussian packets on metric and decorated graphs”, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 372 (2014) | MR | Zbl

[7] V. L. Chernyshev, A. A. Tolchennikov, “Asymptotics of the number of endpoints of a random walk on a certain class of directed metric graphs”, Russ. J. Math. Phys., 28:4 (2021), 434–438 | DOI | MR