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Variational formulas and disorder regimes of random walks in random potentials. (English) Zbl 1368.60105

Two variational formulas are given for the quenched free energy of a random walk in random potential (RWRP) under different conditions. In the directed i.i.d. case, two variational formulas are given for the annealed energy of a RWRP. These four formulas are similar. For each formula, the conditions to have a minimizer are established.

MSC:

60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
60F10 Large deviations
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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