scholarly journals The dual generalized Chernoff inequality for star-shaped curves

2016 ◽  
Vol 40 ◽  
pp. 272-282 ◽  
Author(s):  
Deyan ZHANG ◽  
Yunlong YANG
Keyword(s):  
Chernoff Inequality

scholarly journals On the Spectra of General Random Graphs

10.37236/702 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Fan Chung ◽  
Mary Radcliffe
Keyword(s):  
Independent Random Variable ◽  
Random Graph ◽  
Random Graphs ◽  
Power Law ◽  
Error Bounds ◽  
Adjacency Matrix ◽  
Random Variable ◽  
Degree Sequences ◽  
Chernoff Inequality

We consider random graphs such that each edge is determined by an independent random variable, where the probability of each edge is not assumed to be equal. We use a Chernoff inequality for matrices to show that the eigenvalues of the adjacency matrix and the normalized Laplacian of such a random graph can be approximated by those of the weighted expectation graph, with error bounds dependent upon the minimum and maximum expected degrees. In particular, we use these results to bound the spectra of random graphs with given expected degree sequences, including random power law graphs. Moreover, we prove a similar result giving concentration of the spectrum of a matrix martingale on its expectation.

Binomial Analogues of the Chernoff Inequality

2002 ◽  
Vol 46 (3) ◽  
pp. 544-547 ◽  
Author(s):  
Yu. V. Prokhorov ◽  
O. V. Viskov ◽  
V. I. Khokhlov
Keyword(s):  
Chernoff Inequality

scholarly journals Invertibility of random submatrices via tail-decoupling and a matrix Chernoff inequality

2012 ◽  
Vol 82 (7) ◽  
pp. 1479-1487 ◽  
Author(s):  
Stéphane Chrétien ◽  
Sébastien Darses
Keyword(s):  
Chernoff Inequality

A matrix version of Chernoff inequality

2008 ◽  
Vol 78 (13) ◽  
pp. 1823-1825
Author(s):  
Zhengyuan Wei ◽  
Xinsheng Zhang
Keyword(s):  
Matrix Version ◽  
Chernoff Inequality
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