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First passage percolation on sparse random graphs with boundary weights

Part of: Special processes Mathematical sociology

Published online by Cambridge University Press:  30 July 2019

Lasse Leskelä  and
Hoa Ngo
Lasse Leskelä*
Affiliation:
Aalto University
Hoa Ngo*
Affiliation:
Aalto University
*
*Postal address: Department of Mathematics and Systems Analysis, Aalto University, Otakaari 1, 02015 Espoo, Finland.
**Email address: lasse.leskela@aalto.fi
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Abstract

A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended setting where, in addition, the nodes of the graph are equipped with nonnegative random weights which are used to model the effect of boundary delays across paths in the network. Our main results provide approximative formulas for typical first passage times, typical flooding times, and maximum flooding times in the extended setting, over a time scale logarithmic with respect to the network size.

Keywords

Sparse random graphpercolationfloodingbroadcastingrumor spreadingSI epidemic modelconfiguration modelincubation time

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 91D30: Social networks
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 458 - 471
Copyright
© Applied Probability Trust 2019 

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