Pinsker

Pinsker is a surname of Slavic and Jewish origin. Notable individuals include Isaac Pinsker (1821–1886), a Polish-born Jewish writer and intellectual whose 1882 tract Auto-Emancipation argued for Jewish national revival and is regarded as an early influence on modern Zionism.

In mathematics and information theory, Pinsker's inequality is a fundamental result relating two ways of measuring how different two probability distributions are. For distributions P and Q on a common space, the inequality states that the Kullback–Leibler divergence D_KL(P||Q) provides a lower bound for the square of the total variation distance TV(P,Q): D_KL(P||Q) ≥ 2 [TV(P,Q)]^2. Equivalently, TV(P,Q) ≤ sqrt((1/2) D_KL(P||Q)). The inequality has wide use in probability, statistics, coding theory, and learning theory, where it helps bound approximation error and convergence.

The term Pinsker may also appear in reference to other individuals bearing the surname, and in various mathematical or historical contexts associated with those figures. In general, Pinsker denotes a name connected to both historical biographical work and foundational results in information theory.