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We consider the simple random walk in i.i.d. nonnegative potentials on themultidimensional cubic lattice. Our goal is to investigate the cost paid by thesimple random walk for traveling from the origin to a remote location in alandscape of potentials. In particular, we obtain concentration inequalitiesfor the travel cost in unbounded nonnegative potentials.

Concentrations for the simple random walk in unbounded nonnegative potentials