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We establish the existence of generalized Busemann functions andGibbs-Dobrushin-Landford-Ruelle measures for a general class of lattice randomwalks in random potential with finitely many admissible steps. This classencompasses directed polymers in random environments, first- and last-passagepercolation, and elliptic random walks in both static and dynamic randomenvironments in all dimensions and with minimal assumptions on the randompotential.

Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials