The 123 theorem of Probability Theory and Copositive Matrices
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 ca...
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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2014
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10316/102687 |
| País: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/102687 |
| Resumo: | 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. |
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