The 123 theorem of Probability Theory and Copositive Matrices
Alexander Kovačec ; Miguel M. R. Moreira ; David P. Martins
Special Matrices, Tome 2 (2014), / Harvested from The Polish Digital Mathematics Library
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Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(∥X − Y∥ ≤ b) ≤ c Prob(∥X − Y∥ ≤ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality for monotone functions.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:267310 
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     author = {Alexander Kova\v cec and Miguel M. R. Moreira and David P. Martins},
     title = {The 123 theorem of Probability Theory and Copositive Matrices},
     journal = {Special Matrices},
     volume = {2},
     year = {2014},
     zbl = {1321.60030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0016}
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Alexander Kovačec; Miguel M. R. Moreira; David P. Martins. The 123 theorem of Probability Theory and Copositive Matrices. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0016/

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