  Multielectrode arrays allow recording of the activity of many single neurons,
from which correlations can be calculated. The functional roles of correlations
can be revealed by the measures of the information conveyed by neuronal
activity; a simple formula has been shown to discriminate the information
transmitted by individual spikes from the positive or negative contributions
due to correlations (Panzeri et al, Proc. Roy. Soc. B., {266}: 1001--1012
(1999)). The formula quantifies the corrections to the single-unit
instantaneous information rate which result from correlations in spike emission
between pairs of neurons. Positive corrections imply synergy, while negative
corrections indicate redundancy. Here, this analysis, previously applied to
recordings from small ensembles, is developed further by considering a model of
a large ensemble, in which correlations among the signal and noise components
of neuronal firing are small in absolute value and entirely random in origin.
Even such small random correlations are shown to lead to large possible synergy
or redundancy, whenever the time window for extracting information from
neuronal firing extends to the order of the mean interspike interval. In
addition, a sample of recordings from rat barrel cortex illustrates the mean
time window at which such `corrections' dominate when correlations are, as
often in the real brain, neither random nor small. The presence of this kind of
correlations for a large ensemble of cells restricts further the time of
validity of the expansion, unless what is decodable by the receiver is also
taken into account.
