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We prove an optimal one-volume Wegner estimate for interacting systems of $N$quantum particles moving in the presence of random potentials. The proof isbased on the scale-free unique continuation principle recently developed forthe 1-body problem by Rojas-Molina and Veseli\`c \cite{RM-V1} and extended tospectral projectors by Klein \cite{klein1}. These results extend of ourprevious results in \cite{CHK:2003,CHK:2007}. We also prove a two-volume Wegnerestimate as introduced in \cite{chulaevsky-suhov1}. The random potentials aregeneralized Anderson-type potentials in each variable with minimal conditionson the single-site potential aside from positivity. Under additionalconditions, we prove the Lipschitz continuity of the integrated density ofstates (IDS) This implies the existence and local finiteness of the density ofstates. We also apply these techniques to interacting $N$-particleSchr\"odinger operators with Delone-Anderson type random external potentials.

Optimal Wegner estimate and the density of states for N-body, interacting Schrodinger operators with random potentials