We present a stochastic model based on the Monte Carlo technique to study the inhomogeneous chemical evolution of the Galactic halo. In particular, we consider the local enrichment and subsequent mixing of the interstellar gas resulting from bursts of star formation, following explicitly the fragmentation and coalescence of interstellar gas clouds. The model takes into account the mixing of halo gas through cloud-cloud collisions and the delayed mixing of supernova ejecta into the interstellar medium. The consequences of the infall of halo gas onto the Galactic disk are also discussed. The mass spectrum of clouds, the age-metallicity relation, and the G-dwarf distribution are investigated at different times. We analyze in detail the predictions of our model for the abundance of elements like Eu, Ba, and Sr in the Galactic halo, following their production by $r$-process nucleosynthesis for different assumptions on the supernova mass range. Finally, we compare our results with spectroscopic data for the chemical composition of metal-poor halo stars.
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