  Bird flocks are a paradigmatic example of collective motion. One of the
prominent experimental traits discovered about flocks is the presence of long
range velocity correlations between individuals, which allow them to influence
each other over the large scales, keeping a high level of group coordination. A
crucial question is to understand what is the mutual interaction between birds
generating such nontrivial correlations. Here we use the Maximum Entropy (ME)
approach to infer from experimental data of natural flocks the effective
interactions between birds. Compared to previous studies, we make a significant
step forward as we retrieve the full functional dependence of the interaction
on distance and find that it decays exponentially over a range of a few
individuals. The fact that ME gives a short-range interaction even though its
experimental input is the long-range correlation function, shows that the
method is able to discriminate the relevant information encoded in such
correlations and single out a minimal number of effective parameters. Finally,
we show how the method can be used to capture the degree of anisotropy of
mutual interactions.
