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We provide a simple construction of the Anderson operator in dimensions twoand three. This is done through its quadratic form. We rely on an exponentialtransform instead of the regularity structures or paracontrolled calculus whichare usually used for the construction of the operator. The knowledge of theform is robust enough to deduce important properties such as positivity andirreducibility of the corresponding semigroup. The latter property givesexistence of a spectral gap.

A simple construction of the Anderson operator via its quadratic form in dimensions two and three