Diophantine approximation | Inequalities

Van der Corput inequality

In mathematics, the van der Corput inequality is a corollary of the Cauchy–Schwarz inequality that is useful in the study of correlations among vectors, and hence random variables. It is also useful in the study of equidistributed sequences, for example in the . Loosely stated, the van der Corput inequality asserts that if a unit vector in an inner product space is strongly correlated with many unit vectors , then many of the pairs must be strongly correlated with each other. Here, the notion of correlation is made precise by the inner product of the space : when the absolute value of is close to , then and are considered to be strongly correlated. (More generally, if the vectors involved are not unit vectors, then strong correlation means that .) (Wikipedia).

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Related pages

Corollary | Norm (mathematics) | Random variable | Absolute value | Cauchy–Schwarz inequality | Correlation | Bilinear map | Mathematics | Unit vector | Inner product space | Equidistributed sequence