The property of the remote electron a certain distance away from a Wig
ner crystallized two-dimensional electron system (2DES) is investigate
d. The electron mass of the remote electron is: 1) modified by the per
iodic potential of the Wigner crystal (WC), and 2) renormalized due to
the WC phonons, i.e. the polaron effect. The latter is obtained using
the Feynman path integral method which also provides us with the corr
elation Energy. In this novel polaron problem the electron-phonon inte
raction can be controlled by the distance between the two 2DES.