Context :

Aims : We aim to compute the mass and velocity anisotropy profiles of Abell 2142 and , from there , the pseudo phase–space density profile Q ( r ) and the density slope - velocity anisotropy \beta - \gamma relation , and then to compare them with theoretical expectations .

Methods : The mass profiles were obtained by using three techniques based on member galaxy kinematics , namely the caustic method , the method of Dispersion - Kurtosis , and MAMPOSSt .
Through the inversion of the Jeans equation , it was possible to compute the velocity anisotropy profiles .

Results : The mass profiles , as well as the virial values of mass and radius , computed with the different techniques agree with one another and with the estimates coming from X-ray and weak lensing studies .
A combined mass profile is obtained by averaging the lensing , X-ray , and kinematics determinations .
The cluster mass profile is well fitted by an NFW profile with c = 4.0 \pm 0.5 .
The population of red and blue galaxies appear to have a different velocity anisotropy configuration , since red galaxies are almost isotropic , while blue galaxies are radially anisotropic , with a weak dependence on radius .
The Q ( r ) profile for the red galaxy population agrees with the theoretical results found in cosmological simulations , suggesting that any bias , relative to the dark matter particles , in velocity dispersion of the red component is independent of radius .
The \beta - \gamma relation for red galaxies matches the theoretical relation only in the inner region .
The deviations might be due to the use of galaxies as tracers of the gravitational potential , unlike the non–collisional tracer used in the theoretical relation .

Conclusions :