Optimal paths on the road network as directed polymers
Name
PhysRevE.96.050301.pdf
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2.22 MB
Format
Adobe PDF
Checksum (MD5)
1a8be8bad4fc7d3ae6046ca71a0c3539
Author(s)
Bunin, G.
Solon, Alexandre
Chu, S.
Kardar, Mehran
Date Issued
November 2017
Journal
Physical Review E
Publisher
American Physical Society
Citation
Solon, A. P. et al. "Optimal paths on the road network as directed polymers." Physical Review E 96, 5 (November 2017): 050301(R) © 2017 American Physical Society
Version
Final published version
Abstract
We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. We find that, to a good approximation, the optimal paths can be described as directed polymers in a disordered medium, which belong to the Kardar-Parisi-Zhang universality class of interface roughening. Comparing the scaling behavior of our data with simulations of directed polymers and previous theoretical results, we are able to point out the few characteristics of the road network that are relevant to the large-scale statistics of optimal paths. Indeed, we show that the local structure is akin to a disordered environment with a power-law distribution which become less important at large scales where long-ranged correlations in the network control the scaling behavior of the optimal paths.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.96.050301
