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Sharp bounds on the variance in randomized experiments

✍ Scribed by Aronow, Peter M.; Green, Donald P.; Lee, Donald K. K.


Book ID
125462280
Publisher
Institute of Mathematical Statistics
Year
2014
Tongue
English
Weight
218 KB
Volume
42
Category
Article
ISSN
0090-5364

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Sharp bounds on the eigenvalues of trees
✍ Shengbiao Hu πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 289 KB

Let Ξ» 1 (T ) and Ξ» 2 (T ) be the largest and the second largest eigenvalues of a tree T , respectively. We obtain the following sharp lower bound for Ξ» 1 (T ): where d i is the degree of the vertex v i and m i is the average degree of the adjacent vertices of v i . Equality holds if and only if T i