2012/01/25 by Guy Fayolle, Fayolle, Guy, Cyril Furtlehner +1
Computer Science · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Topological and Geometric Data Analysis #advanced mathematical theories #math.PR
paper · pdf · doi:10.48550/arxiv.1201.5185
Proceedings on CD. ISBN 978-5-901158-15-9; Int. Math. Conf. "50 Years of IPPI" (2011)
arxiv created 2012/01/25 · openalex publication_date 2012/01/25 · arxiv updated 2012/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate goal being to derive hydrodynamic limits after proper scalings. A seemingly new method is proposed, which relies on the analysis of specific partial differential operators, involving variational calculus and functional integration: indeed, the variables are the values of some functions at given points, the number of which tends to become infinite, which requires the construction of generalized measures. Starting from a detailed analysis of the asep system on the torus Z/N/Z, we claim that the arguments a priori work in higher dimensions (ABC, multi-type exclusion processes, etc), leading to sytems of coupled partial differential equations of Burgers' type.