Fermionic construction of tau functions and random processes

Details Fermionic construction of tau functions and random processes Fermionic construction of tau functions and random processes

2007-04-09

arxiv.org/abs/0704.1157v1

Physica D: 235 (2007) 168-206

Physics

Mathematical Physics

53 pages, 13 figures, a contribution to Proc. "Mathematics and Physics of Growing Interfaces"

Scientific paper

10.1016/j.physd.2007.05.011

Tau functions expressed as fermionic expectation values are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the integer lattice, like a discrete version simple exclusion processes (ASEP), nonintersecting random walkers, lattice Coulomb gas models and others, as well as providing a powerful tool for combinatorial calculations involving paths between pairs of partitions. We study the decay of the initial step function within the discrete ASEP (d-ASEP) model as an example.

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