אריה קנטורוביץ

If one seeks to estimate the total variation between two product measures (formula Presented) in terms of their marginal TV sequence (Math Presented) then trivial upper and lower bounds are provided by (formula Presented) We improve the lower bound to (formula Presented) TV, there by reducing the gap between the upper and lower bounds from (formula Presented) Furthermore, we show that any estimate on (formula Presented) expressed in terms of δ must necessarily exhibit a gap of (formula Presented) between the upper and lower bounds in the worst case, establishing a sense in which our estimate is optimal. Finally, we identify a natural class of distributions for which (formula Presented) approximates the TV distance up to absolute multiplicative constants.