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

Concentrations for the simple random walk in un- bounded nonnegative potentials