  Let $\mathfrak{g}$ be a semisimple Lie algebra, $\mathfrak{t}$ its Cartan
subalgebra and $W$ the Weyl group.
  The goal of this paper is to prove an isomorphism between suitable
completions of the equivariant Borel-Moore homology of certain affine Springer
fibers for $\mathfrak{g}$ and the global sections of a bundle related to a
Procesi bundle on the smooth locus of a partial resolution of
$(\mathfrak{t}\oplus \mathfrak{t}^*)/W$. We deduce some applications of our
isomorphism including a conditional application to the center of the small
quantum group. Our main method is to compare certain bimodules over rational
and trigonometric Cherednik algebras.
