Interaction potential (source code)

= Interaction potential
{title2=$W:\mathbb R^d\to\mathbb R$}

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>.