Aaron O. - The IceCube neutrino telescope has detected a diffuse flux of high-energy astrophysical neutrinos, but the sources of this flux have largely remained elusive. Using the 10-year IceCube public dataset, we search for correlations between neutrino events and tracers of large-scale structure (LSS). We conduct a combined cross-correlation analysis using several all-sky galaxy catalogs spanning a broad redshift range and maps of the cosmic infrared background. We do not detect a definitive signal, but find tantalizing hints of a potential positive correlation between neutrinos and the tracers of LSS. We additionally construct a simple model to interpret the galaxy-neutrino cross-correlations in terms of the redshift distribution of neutrino sources. We put upper limits on the clustering amplitude of neutrinos based on the measured cross-correlations with galaxies and forecast the improvements on these constraints that can be obtained using future detectors. We show that, in the future, neutrino-galaxy cross-correlations should be a powerful probe to constrain properties of neutrino source populations.