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Stochastic dynamics of discrete curves and multi-type exclusion processes. (English) Zbl 1126.82022

The paper deals with curve stochastic deformations which are defined by a rotating vector with the polar angle \(2k\pi/n\) where \(k\) and \(n\) denote integers, referred to as a stochastic clock model of deformation. For reversible systems, one shows that the limiting invariant measure is the solution of a nonlinear differential Lotka-Volterra system. The study is a bit more complex for dynamics in which the invariant measure is not described by means of a potential. In this case, one uses combinatorial formulae to define the invariant measure and by this way one can obtain some results on cycle currents and fluid limits (hydrodynamic currents). Then one derives relationships between currents and particle densities at the deterministic level by using the law of large numbers, and lastly one computes the stochastic corrections for these relations by using a central limit theorem for current.

MSC:

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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