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We use a high resolution collisionless simulation of a Virgo--like cluster ina $\Lambda$CDM cosmology to determine the velocity and clustering properties ofthe diffuse stellar component in the intracluster region at the present epoch.The simulated cluster builds up hierarchically and tidal interactions betweenmember galaxies and the cluster potential produce a diffuse stellar componentfree-flying in the intracluster medium. Here we adopt an empirical scheme toidentify tracers of the stellar component in the simulation and hence study itsproperties. We find that at $z=0$ the intracluster stellar light is mostlyunrelaxed in velocity space and clustered in structures whose typicalclustering radii are about 50 kpc at R=400--500 kpc from the cluster center,and predict the radial velocity distribution expected in spectroscopicfollow-up surveys. Finally, we compare the spatial clustering in the simulationwith the properties of the Virgo intracluster stellar population, as traced byongoing intracluster planetary nebulae surveys in Virgo. The preliminaryresults indicate a substantial agreement with the observed clusteringproperties of the diffuse stellar population in Virgo.Comment: 39 pages, 10 figures, 8 tables, in press on ApJ. Bad image quality  for some figures because resizing is neede

Intracluster Stellar Population Properties fromN‐Body Cosmological Simulations. I. Constraints atz= 0