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Title:
Totally Asymmetric Models as Generators of Oriented Multi-Dimensional
Random Walks
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Abstract:
The exactly solvable totally asymmetric models of the low dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonians are considered. We demonstrate that the conditional probabilities of the Totally Asymmetric Zero Range Process and Totally Asymmetric Simple Exclusion Process may be considered as the generating functions of oriented multi-dimensional lattice walks bounded by a hyperplane. This type of walks we call the walks over the multi-dimensional simplicial lattices. The answers for the conditional probability and for the number of random walks over the multi-dimensional simplicial lattice are expressed through the symmetric functions.
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