Document Type : Original Article


Department of Physics, University of Tehran, Tehran 14395-547, Iran


In this paper, we introduce a percolation model consisting of random walk movements on a lattice.
Random walk not only has local movements, but also has non-local movements on the lattice. We obtain
the percolation transitions and critical exponents for this model. Our findings show that the percolation
threshold decreases with increasing non-local movements. Also, we find the universal scaling functions
for the size of the largest gap and biggest cluster by the extreme value theory.


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