  We discuss the question of recurrence for persistent, or Newtonian, random
walks in Z^2, i.e., random walks whose transition probabilities depend both on
the walker's position and incoming direction. We use results by Toth and
Schmidt-Conze to prove recurrence for a large class of such processes,
including all "invertible" walks in elliptic random environments. Furthermore,
rewriting our Newtonian walks as ordinary random walks in a suitable graph, we
gain a better idea of the geometric features of the problem, and obtain further
examples of recurrence.
