Improving constant in end-point Poincaré inequality on Hamming cube

Paata Ivanisvili, Dong Li, Ramon van Handel +1

We improve the constant $\frac{\pi }{2}$ in $L^1$-Poincaré inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\sqrt{\frac{\pi }{2}}$.…