Transient Nearest Neighbor Random Walk on the Line
✍ Scribed by Endre Csáki; Antónia Földes; Pál Révész
- Publisher
- Springer US
- Year
- 2008
- Tongue
- English
- Weight
- 392 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0894-9840
No coin nor oath required. For personal study only.
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The bipartite kth nearest neighbor graphs B are studied. It is shown that B k 1 has a limiting expected matching number of approximately 80% of its vertices, that with high Ž . probability whp B has at least 2 log nr13 log log n vertices not matched, and that whp B 2 3 does have a perfect matching.
Random nearest neighbor and influence graphs with vertex set Z d are defined and their percolation properties are studied. The nearest neighbor graph has (with probability 1) only finite connected components and a superexponentially decaying connectivity function. Influence graphs (which are related