 Interaction potential

A function assigning energy to the separation of two particles. The common symmetric case is an even function, $W(z)=W(-z)$. Its average over pairs defines an interaction energy. If the Hessian matrix is bounded, the gradient is globally Lipschitz and grows at most linearly; its convolution with a probability measure therefore needs only a finite first absolute moment, even though the potential itself can require a second absolute moment.