  We investigate correlation between the arrival directions of
ultra-high-energy cosmic rays (UHECRs) and the large-scale structure (LSS) of
the Universe by using statistical quantities which can find the angular scale
of the correlation. The Infrared Astronomical Satellite Point Source Redshift
Survey (IRAS PSCz) catalog of galaxies is adopted for LSS. We find a positive
correlation of the highest energy events detected by the Pierre Auger
Observatory (PAO) with the IRAS galaxies inside $z=0.018$ within the angular
scale of $\sim 15^{\circ}$. This positive correlation observed in the southern
sky implies that a significant fraction of the highest energy events comes from
nearby extragalactic objects. We also analyze the data of the Akeno Giant Air
Shower Array (AGASA) which observed the northern hemisphere, but the obvious
signals of positive correlation with the galaxy distribution are not found.
Since the exposure of the AGASA is smaller than the PAO, the cross-correlation
in the northern sky should be tested using a larger number of events detected
in the future. We also discuss the correlation using the all-sky combined data
sets of both the PAO and AGASA, and find a significant correlation within $\sim
8^{\circ}$. These angular scales can constrain several models of intergalactic
magnetic field. These cross-correlation signals can be well reproduced by a
source model in which the distribution of UHECR sources is related to the IRAS
galaxies.
