Universität zu Köln

Hwang, S., Lee, D. -S. and Kahng, B. (2014). Blind and myopic ants in heterogeneous networks. Phys. Rev. E, 90 (5). COLLEGE PK: AMER PHYSICAL SOC. ISSN 1550-2376

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Abstract

The diffusion processes on complex networks may be described by different Laplacian matrices due to heterogeneous connectivity. Here we investigate the random walks of blind ants and myopic ants on heterogeneous networks: While a myopic ant hops to a neighbor node every step, a blind ant may stay or hop with probabilities that depend on node connectivity. By analyzing the trajectories of blind ants, we show that the asymptotic behaviors of both random walks are related by rescaling time and probability with node connectivity. Using this result, we show how the small eigenvalues of the Laplacian matrices generating the two random walks are related. As an application, we show how the return-to-origin probability of a myopic ant can be used to compute the scaling behaviors of the Edwards-Wilkinson model, a representative model of load balancing on networks.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hwang, S. UNSPECIFIED UNSPECIFIED UNSPECIFIED Lee, D. -S. UNSPECIFIED UNSPECIFIED UNSPECIFIED Kahng, B. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-423183
DOI:	10.1103/PhysRevE.90.052814
Journal or Publication Title:	Phys. Rev. E
Volume:	90
Number:	5
Date:	2014
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	1550-2376
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language RANDOM-WALKS; ANOMALOUS DIFFUSION; 1ST-PASSAGE TIMES; COMPLEX NETWORKS; NAVIGABILITY; WORLD Multiple languages Physics, Fluids & Plasmas; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/42318