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Hao, Nannan; Heydenreich, Markus ORCID: 0000-0002-3749-7431 (2023): Graph distances in scale-free percolation: the logarithmic case. In: Journal of Applied Probability, Vol. 60, No. 1: pp. 295-313
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Scale-free percolation is a stochastic model for complex networks. In this spatial random graph model, vertices x,y∈Zd are linked by an edge with probability depending on independent and identically distributed vertex weights and the Euclidean distance |x−y| . Depending on the various parameters involved, we get a rich phase diagram. We study graph distance and compare it to the Euclidean distance of the vertices. Our main attention is on a regime where graph distances are (poly-)logarithmic in the Euclidean distance. We obtain improved bounds on the logarithmic exponents. In the light tail regime, the correct exponent is identified.