Convex Poincaré inequality
arXiv:1310.1881
Abstract
We characterize the symmetric measures which satisfy the one dimensional convex Poincaré inequality. For these measures the tenesorization argument yields concentration inequalities for their products and convex sets in R^n.
This paper has been withdrawn as it turned out that the result is known due to the work S. Bobkov, F. Götze, Discrete isoperimetric and Poincaré-type inequalities, Probab. Theory Related Fields 114 (1999), no. 2, 245-277