Aims: We use the VVDS-Deep first-epoch data to measure the dependence of galaxy clustering on galaxy stellar mass, at z~0.85. Methods: We measure the projected correlation function wp(rp) for sub-samples with 0.5<z<1.2 covering different mass ranges between 10^9 and 10^11 Msun. We quantify in detail the observational selection biases using 40 mock catalogues built from the Millennium run and semi-analytic models. Results: Our simulations indicate that serious incompleteness in mass is present only for log(M/Msun)<9.5. In the mass range log(M/Msun)=[9.0-9.5], the photometric selection function of the VVDS misses 2/3rd of the galaxies. The sample is virtually 100% complete above 10^10 Msun. We present the first direct evidence for a clear dependence of clustering on the galaxy stellar mass at z~0.85. The clustering length increases from r0 ~ 2.76 h^-1 Mpc for galaxies with mass M>10^9 Msun to r0 ~ 4.28 h^-1 Mpc for galaxies more massive than 10^10.5 Msun. At the same time, the slope increases from ~ 1.67 to ~ 2.28. A comparison of the observed wp(rp) to local measurements by the SDSS shows that the evolution is faster for objects less massive than ~10^10.5 Msun. This is interpreted as a higher dependence on redshift of the linear bias b_L for the more massive objects. While for the most massive galaxies b_L decreases from 1.5+/-0.2 at z~0.85 to 1.33+/-0.03 at z~0.15, the less massive population maintains a virtually constant value b_L~1.3. This result is in agreement with a scenario in which more massive galaxies formed at high redshift in the highest peaks of the density field, while less massive objects form at later epochs from the more general population of dark-matter halos.
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