  Information on the structure around active galactic nuclei (AGN) has long
been derived from measuring lags in their varying light output at different
wavelengths. In principle, infrared data would reach to larger radii,
potentially even probing reprocessed radiation in any surrounding dusty torus.
In practice, this has proved challenging because high quality data are required
to detect such variability, and the observations must stretch over a long
period to probe the likely month-scale lags in variability. In addition, large
numbers of sources would need to be observed to start searching for any
patterns in such lags. Here, we show that the UKIDSS Ultra Deep Survey, built
up from repeated observations over almost a decade, provides an ideal data set
for such a study. For 94 sources identified as strongly-varying AGN within its
square-degree field, we find that the K-band light curves systematically lag
the J-band light curves by an average of around a month. The lags become
smaller at higher redshift, consistent with the band shift to optical
rest-frame emission. The less luminous AGN also display shorter lags, as would
be expected if their physical size scales with luminosity.
