  Colloidal systems observed in video microscopy are often analysed using the
displacements correlation matrix of particle positions. In non-thermal systems,
the inverse of this matrix can be interpreted as a pair-interaction potential
between particles. If the system is thermally agitated, however, only an
effective interaction is accessible from the correlation matrix. We show how
this effective interaction differs from the non-thermal case by comparing with
high-statistics numerical data from hard-sphere crystals.
