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Stochastic Dynamics of Discrete Curves and Exclusion Processes. Part 2: Functional Equations and Continuous Descriptions

Abstract : This report deals with continuous limits of several one-dimensional diffusive systems, obtained from stochastic distortions of discrete curves with different kinds of coding. These systems are indeed special cases of reaction-diffusion. A general functional formalism is set up, allowing to grapple with hydrodynamic limits. We also analyse the steady-state regime, not only in the reversible case, so that the invariant measure can have a non Gibbs form. A link is made between recursion properties, which originate matrix solutions, and particle cycles in the state-graph, by introducing loop currents on the analogy with electric circuits. Also, by means of the aforementioned functional approach, a bridge is established between structural constants involved in the recursions at discrete level and the constants which appear in Lotka-Volterra equations describing the fluid limits of stationary states. Finally the Lagrangian for the current fluctuations is obtained from an iterative scheme, and the related Hamilton-Jacobi equation, leading to the large deviation functional, is solved at least in the reversible case allowing to rediscover some known results.
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Submitted on : Friday, May 19, 2006 - 7:31:00 PM
Last modification on : Thursday, February 3, 2022 - 11:14:13 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:37:22 PM

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Guy Fayolle, Cyril Furtlehner. Stochastic Dynamics of Discrete Curves and Exclusion Processes. Part 2: Functional Equations and Continuous Descriptions. [Research Report] RR-5808, INRIA. 2006, pp.67. ⟨inria-00070216⟩

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