Geometric and Functional Inequalities for Log-concave Probability Sequences
| Autor: | Marsiglietti, Arnaud, Melbourne, James |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the integers. A functional analogue of this geometric inequality is derived, giving large and small deviation inequalities from a median, in terms of a modulus of regularity. Our methods are of independent interest, we find that log-affine sequences are the extreme points of the set of log-concave sequences belonging to a half-space slice of the simplex. We use this result as a tool to derive simple proofs of several convolution type inequalities for log-concave sequences, due to Walkup, Gurvits, and Klartag-Lehec. Further applications of our results are used to produce a discrete version of the Pr\'ekopa-Leindler inequality. Comment: 27 pages |
| Databáze: | arXiv |
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