We present numerical simulations on propagation of Ultra-High Energy Cosmic Rays ( UHECRs ) above 10 ^ { 19 } eV in a structured extragalactic magnetic field ( EGMF ) and simulate their arrival distributions at the earth .
We use the IRAS PSCz catalogue in order to construct a model of the EGMF and source models of UHECRs , both of which reproduce the local structures observed around the Milky Way .
We also consider modifications of UHECR arrival directions by the galactic magnetic field .
We follow an inverse process of their propagation from the earth and record the trajectories .
This enables us to calculate only trajectories of UHECRs arriving at the earth , which saves the CPU time .
From these trajectories and our source models , we construct arrival distributions of UHECRs and calculate the harmonic amplitudes and the two point correlation functions of them .
We estimate number density of sources which reproduces the Akeno Ground Air Shower Array ( AGASA ) observation best .
As a result , we find that the most appropriate number density of the sources is \sim 5 \times 10 ^ { -6 } Mpc ^ { -3 } .
This constrains the source candidates of UHECRs .
We also demonstrate skymaps of their arrival distribution with the event number expected by future experiments and examine how the EGMF affects their arrival distribution .
A main result is diffusion of clustering events which are obtained from calculations in the absence of the EGMF .
This tendency allows us to reproduce the observed two point correlation function better .