# Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics

Volchenkov D, Blanchard P (2007)

Physical Review E 75(2): 6104-6118.

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Abstract

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an informationlike parameter which plays the role of an individual fingerprint of Genius loci. Global structural properties of a city can be characterized by the thermodynamic parameters calculated in the random walk problem.

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Volchenkov D, Blanchard P. Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*. 2007;75(2):6104-6118.Volchenkov, D., & Blanchard, P. (2007). Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*,*75*(2), 6104-6118. doi:10.1103/PhysRevE.75.026104Volchenkov, D., and Blanchard, P. (2007). Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*75, 6104-6118.Volchenkov, D., & Blanchard, P., 2007. Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics.

*Physical Review E*, 75(2), p 6104-6118. D. Volchenkov and P. Blanchard, “Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics”,

*Physical Review E*, vol. 75, 2007, pp. 6104-6118. Volchenkov, D., Blanchard, P.: Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics. Physical Review E. 75, 6104-6118 (2007).

Volchenkov, Dimitry, and Blanchard, Philippe. “Random walks along the streets and canals in compact cities: Spectral analysis, dynamical modularity, information, and statistical mechanics”.

*Physical Review E*75.2 (2007): 6104-6118.
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