Giant component of the soft random geometric graph

نویسندگان

چکیده

Consider a 2-dimensional soft random geometric graph G(λ,s,ϕ), obtained by placing Poisson(λs2) number of vertices uniformly at in square side s, with edges placed between each pair x,y probability ϕ(‖x−y‖), where ϕ: R+→[0,1] is finite-range connection function. This paper concerned the asymptotic behaviour G(λ,s,ϕ) large-s limit (λ,ϕ) fixed. We prove that proportion largest component converges to percolation for corresponding model, which defined similarly Poisson process on whole plane. do not cover case λ equals critical value λc(ϕ).

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ژورنال

عنوان ژورنال: Electronic Communications in Probability

سال: 2022

ISSN: ['1083-589X']

DOI: https://doi.org/10.1214/22-ecp491