Bootstrap multiscale analysis and localization for multi-particle continuous Anderson Hamiltonians (Q2515803)

The bootstrap multiscale analysis, developed in the one-particle case by \textit{F. Germinet} and \textit{A. Klein} [Commun. Math. Phys. 222, No. 2, 415--448 (2001; Zbl 0982.82030)], is an enhanced multiscale analysis that yields sub-exponentially decaying probabilities for ``bad'' events. Later, the authors of this paper extended the bootstrap multiscale analysis to the multi-particle (discrete) Anderson model [J. Stat. Phys. 151, No. 5, 938--973 (2013; Zbl 1272.82021)]. In this article, they extend the bootstrap multiscale analysis and its consequences to the multi-particle (continuous) Anderson Hamiltonian. They also extend the unique continuation principle for spectral projections of Schrödinger operators to arbitrary rectangles, and use it to prove Wegner estimates for multi-particle continuous Anderson Hamiltonians without the requirement of a covering condition.