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We study a system of $N$ interacting fermions at positive temperature in aconfining potential. In the regime where the intensity of the interactionscales as $1/N$ and with an effective semi-classical parameter $\hbar=N^{-1/d}$where $d$ is the space dimension, we prove the convergence to the correspondingThomas-Fermi model at positive temperature.

Semi-classical limit of large fermionic systems at positive temperature