Khinchine type inequalities with optimal constants via ultra log-concavity
We derive Khinchine type inequalities for even moments with optimal constants from the result of Walkup (J Appl Probab 13:76–85, 1976) which states that the class of log-concave sequences is closed under the binomial convolution.
KeywordsLog-concavity Ultra log-concavity Khinchine inequality Factorial moments
Mathematics Subject Classification (2000)60E15 26D15
We are grateful to Matthieu Fradelizi and Olivier Guédon for pointing to us the article of Walkup, and for their help in tracing some other references.
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- 4.Czerwiński, W.: Khinchine inequalities (in Polish). University of Warsaw, Master thesis (2008)Google Scholar
- 5.Gurvits, L.: A short proof, based on mixed volumes, of Liggett’s theorem on the convolution of ultra-logconcave sequences. Electron. J. Combin. 16, Note 5 (2009)Google Scholar
- 13.Oleszkiewicz, K.: Comparison of moments via Poincaré-type inequality. In: Advances in Stochastic Inequalities (Atlanta, GA, 1997), Contemp. Math. 234. American Mathematical Society, Providence 135–148 (1999)Google Scholar