Local energy statistics in directed polymers.
Random walks in with non-zero drift absorbed at the axes
Spatially homogeneous random walks in with non-zero jump probabilities at distance at most , with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.
Derrida's generalised random energy models 1 : models with finitely many hierarchies
Derrida's generalized random energy models 2 : models with continuous hierarchies
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