Logarithmic scaling of planar random walk's local times
  We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the $M1$ topology and fails to hold in the $J1$ topology. 
P\'eter N\'andori, Zeyu Shen
math.PR