We present the first measurement of the fluctuations in the number of muons
in extensive air showers produced by ultra-high energy cosmic rays. We find
that the measured fluctuations are in good agreement with predictions from air
shower simulations. This observation provides new insights into the origin of
the previously reported deficit of muons in air shower simulations and
constrains models of hadronic interactions at ultra-high energies. Our
measurement is compatible with the muon deficit originating from small
deviations in the predictions from hadronic interaction models of particle
production that accumulate as the showers develop.Comment: Accepted for publication in PR