Hormann, Erik, Lambiotte, Renaud, and Cantwell, George T. (2025) Approximation for return time distributions of random walks on sparse networks. Physical Review E, 111. 064306.

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Abstract

We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation to account for the short- and long-term behaviors, respectively. We test this approximation on several classes of large graphs and find excellent agreement between our approximations and the true distributions. While the statistical properties of a random walk will depend on the structure of the network, the observed agreement between our approximations and numerical calculations implies that while local structure is clearly very influential, global structure is only important in a relatively superficial way, namely through the total number of edges.

Item ID:	91262
Item Type:	Article (Research - C1)
ISSN:	2470-0045
Copyright Information:	Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Date Deposited:	28 Apr 2026 23:53
FoR Codes:	49 MATHEMATICAL SCIENCES > 4902 Mathematical physics > 490206 Statistical mechanics, physical combinatorics and mathematical aspects of condensed matter @ 50% 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490104 Complex systems @ 50%
SEO Codes:	28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences @ 50% 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280120 Expanding knowledge in the physical sciences @ 50%
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