Random collisions on branched networks: How simultaneous diffusion prevents encounters in inhomogeneous structures
Name
Campari-2012-Random collisions on branched networks.pdf
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392.07 KB
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Checksum (MD5)
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Author(s)
Campari, Riccardo
Cassi, Davide
Date Issued
August 2012
Journal
Physical Review E
Publisher
American Physical Society
Citation
Campari, Riccardo, and Davide Cassi. “Random Collisions on Branched Networks: How Simultaneous Diffusion Prevents Encounters in Inhomogeneous Structures.” Physical Review E 86.2 (2012). ©2012 American Physical Society
Version
Final published version
Abstract
A huge variety of natural phenomena, including prey-predator interaction, chemical reaction kinetics, foraging, and pharmacokinetics, are mathematically described as encounters between entities performing a random motion on an appropriate structure. On homogeneous structures, two random walkers meet with certainty if and only if the structure is recurrent, i.e., a single random walker returns to its starting point with probability 1. We prove here that this property does not hold on general inhomogeneous structures, and introduce the concept of two-particle transience, providing examples of realistic recurrent structures where two particles may never meet if they both move, while an encounter is certain if either stays put. We anticipate that our results will pave the way for the study of the effects of geometry in a wide array of natural phenomena involving interaction between randomly moving agents.
MIT Department
Massachusetts Institute of Technology. Department of Urban Studies and Planning
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.86.021110
