Graph diameter in long-range percolation
نویسنده
چکیده
We study the asymptotic growth of the diameter of the graph obtained by adding sparse “long” edges to a square box in Z. We focus on the cases when an edge between x and y is added with probability decaying with their Euclidean distance like |x − y| as |x − y| → ∞. For s ∈ (d, 2d) we show that the graph diameter for a box of side L scales like (logL) where ∆ = log2(2d/s). In other words, the diameter grows about as fast as the graph distance between two “typical” points in the box.
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ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 39 شماره
صفحات -
تاریخ انتشار 2011