  We develop a method based on the collisionless Boltzmann equation to
calculate the gravitational clustering of relic neutrinos in realistic
cosmological models dominated by cold dark matter (CDM) and the cosmological
constant. This method can be used to estimate the phase-space distribution of
any light particles in CDM halos. We find that neutrinos with masses > 0.3 eV
cluster appreciably in dark matter halos above the galactic size. The resulting
neutrino overdensity above the cosmic mean neutrino density increases with both
the neutrino mass and the halo mass, ranging from about 10 for 0.3 eV neutrinos
in 10^13 M_sun halos, to about 1500 for 1.8 eV neutrinos in 10^15 M_sun halos.
We examine the implications of neutrino clustering for the Z-burst model of
ultra high energy cosmic rays (UHECR), which interprets the observed events at
E > 4 x 10^19 eV as decay products of Z-bosons from the resonant scattering
between relic and high energy neutrinos and anti-neutrinos. We estimate the
UHECR energy spectrum for various neutrino masses towards five of the most
massive clusters in the local universe (within 100 Mpc): Virgo, Perseus-Pisces,
Hydra, Centaurus, and Coma. The UHECR flux in the Z-burst model is expected to
be significantly higher towards these clusters if m_nu > 0.3 eV and nearly
isotropic otherwise.
