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math.PR2019
Global observables for random walks: law of large numbers
Dmitry Dolgopyat, Marco Lenci, Péter Nándori
We consider the sums where is a random walk on and is a global observable, that is, a bounded function wh…
math.PR2016
Logarithmic scaling of planar random walk's local times
Péter Nándori, Zeyu Shen
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 pla…