Local Central Limit Theorem for a Random Walk Perturbed in One Point
  We consider a symmetric random walk on the $\nu$-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction to diffusive behaviour appears in any dimension along with a long-range correction in the one-dimensional case. 
Giuseppe Genovese and Renato Luc\`a
math.PR