On Central Limit Theorems in Geometrical Probability
On Central Limit Theorems in Geometrical Probability
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, points which are neighbors in the MST have to be also Voronoi neighbors (see figure 1). This property leads to an efficient algorithm for the MST, since one first constructs the Delaunay triangulation in O(nlogn) time and then runs the greedy algorithm on its graph, leading to an O(nlogn) algorithm for the MST as well. Figure 1: The Voronoi diagram and the Delaunay triangulation We believe that our results give some partial insight on why a CLT might hold for the MST as well. Ramey [10] has a...ttempted to prove a CLT for the MST, but his approach, although very interesting, did not succeed since he needed some unproven, but plausible, lemmas from continuous percolation. Figure 2: The MST is a subgraph of the Delaunay triangulation The CLT for jVi, „ has already been obtained by Bickel and Breiman [5], who used very complicated fourth moment estimates. They wrote: "Our proof is long. We believe that this is due to the complexity of the problem. Nearest neighbor distances are not independent".
What to read after On Central Limit Theorems in Geometrical Probability?
You can find similar books in the "Read Also" column, or choose other free books by Florin Avram to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, points which are neighbors in the MST have to be also Voronoi neighbors (see figure 1). This property leads to an efficient algorithm for the MST, since one first constructs the Delaunay triangulation in O(nlogn) time and then runs the greedy algorithm on its graph, leading to an O(nlogn) algorithm for the MST as well. Figure 1: The Voronoi diagram and the Delaunay triangulation We believe that our results give some partial insight on why a CLT might hold for the MST as well. Ramey [10] has a...ttempted to prove a CLT for the MST, but his approach, although very interesting, did not succeed since he needed some unproven, but plausible, lemmas from continuous percolation. Figure 2: The MST is a subgraph of the Delaunay triangulation The CLT for jVi, „ has already been obtained by Bickel and Breiman [5], who used very complicated fourth moment estimates. They wrote: "Our proof is long. We believe that this is due to the complexity of the problem. Nearest neighbor distances are not independent".
What to read after On Central Limit Theorems in Geometrical Probability?
You can find similar books in the "Read Also" column, or choose other free books by Florin Avram to read onlineMoreLess
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