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Self-averaging : ウィキペディア英語版 | Self-averaging A self-averaging physical property of a disordered system is one that can be described by averaging over a sufficiently large sample. The concept was introduced by Ilya Mikhailovich Lifshitz. == Definition ==
Frequently in physics one comes across situations where quenched randomness plays an important role. Any physical property ''X'' of such a system, would require an averaging over all disorder realisations. The system can be completely described by the average () where () denotes averaging over realisations (“averaging over samples”) provided the relative variance ''R''''X'' = ''V''''X'' / ()2 → 0 as ''N''→∞, where ''V''''X'' = () − ()2 and ''N'' denotes the size of the realisation. In such a scenario a single large system is sufficient to represent the whole ensemble. Such quantities are called self-averaging. Away from criticality, when the larger lattice is built from smaller blocks, then due to the additivity property of an extensive quantity, the central limit theorem guarantees that ''R''''X'' ~ ''N''−1 thereby ensuring self-averaging. On the other hand, at the critical point, the question whether is self-averaging or not becomes nontrivial, due to long range correlations.
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