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- W4293496937 abstract "Consider~(n) nodes distributed independently across~(N) cities contained with the unit square~(S) according to a distribution~(f.) Each city is modelled as an~(r_n times r_n) square contained within~(S) and~(MSTC_n) denotes the length of the minimum spanning tree containing all the~(n) nodes. We use approximation methods to obtain variance estimates for~(MSTC_n) and prove that if the cities are well-connected and densely populated in a certain sense, then~(MSTC_n) appropriately centred and scaled converges to zero in probability. Using the proof techniques, we alternately derive corresponding results for the length~(MST_n) of the minimum spanning tree for the usual case when the nodes are independently distributed throughout the unit square~(S.) In particular, we obtain that the variance of~(MST_n) grows at most as a power of the logarithm of~(n) and use a subsequence argument to get almost sure convergence of~(MST_n) appropriately centred and scaled." @default.
- W4293496937 created "2022-08-29" @default.
- W4293496937 creator A5090101166 @default.
- W4293496937 date "2018-01-08" @default.
- W4293496937 modified "2023-09-27" @default.
- W4293496937 title "Minimum spanning trees across dense cities" @default.
- W4293496937 doi "https://doi.org/10.48550/arxiv.1801.02697" @default.
- W4293496937 hasPublicationYear "2018" @default.
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