Stochastic Dynamics of Discrete Curves and Multi-type Exclusion Processes

Abstract

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a reaction-diffusion nature. In the non-reversible case, the invariant measure has generally a non Gibbs form. The corresponding steady-state regime is analyzed in detail with the help of a tagged particle and a state-graph cycle expansion of the probability currents. As a consequence, the constants appearing in Lotka-Volterraequations --which describe the fluid limits of stationary states-- can be traced back directly at the discrete level to tagged particles cycles coefficients. Current fluctuations are also studied and the Lagrangian is obtained by an iterative scheme. The related Hamilton-Jacobi equation, which leads to the large deviation functional, is analyzed and solved in the reversible case for the sake of checking.

Short version of Inria Reasearch Report, 33 pages, 6 figures. submited to J.Stat.Phys

References in corpus (3)

• Macroscopic current fluctuations in stochastic lattice gases
• Stationary distributions of multi-type totally asymmetric exclusion processes
• Stochastic Dynamics of Discrete Curves and Exclusion Processes. Part 1: Hydrodynamic Limit of the ASEP System

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• Phase diagram of the ABC model with nonconserving processes
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• The grand canonical ABC model: a reflection asymmetric mean field Potts model
• Anomalous long-range correlations at a non-equilibrium phase transition
• Phase diagram of a generalized ABC model on the interval
• Drift of phase fluctuations in the ABC model
• The energy of the alphabet model