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Full-Text Articles in Physical Sciences and Mathematics
Numerical And Statistical Methods For The Coarse-Graining Of Many-Particle Stochastic Systems, Ma Katsoulakis, P Plechac, L Rey-Bellet
Numerical And Statistical Methods For The Coarse-Graining Of Many-Particle Stochastic Systems, Ma Katsoulakis, P Plechac, L Rey-Bellet
Luc Rey-Bellet
In this article we discuss recent work on coarse-graining methods for microscopic stochastic lattice systems. We emphasize the numerical analysis of the schemes, focusing on error quantification as well as on the construction of improved algorithms capable of operating in wider parameter regimes. We also discuss adaptive coarse-graining schemes which have the capacity of automatically adjusting during the simulation if substantial deviations are detected in a suitable error indicator. The methods employed in the development and the analysis of the algorithms rely on a combination of statistical mechanics methods (renormalization and cluster expansions), statistical tools (reconstruction and importance sampling) and …
Multibody Interactions In Coarse-Graining Schemes For Extended Systems, S Are, Ma Katsoulakis, P Plechac, L Rey-Bellet
Multibody Interactions In Coarse-Graining Schemes For Extended Systems, S Are, Ma Katsoulakis, P Plechac, L Rey-Bellet
Luc Rey-Bellet
In this paper we address the role of multibody interactions for the coarse-grained approximation of stochastic lattice systems. Such interaction potentials are often not included in coarse-graining schemes, as they can be computationally expensive. The multibody interactions are obtained from the error expansion of the reference measure which is, in many cases, chosen as a Gibbs measure corresponding to a local mean-field approximation. We identify the parameter $\epsilon$ that characterizes the level of approximation and its relation to the underlying interaction potential. The error analysis suggests strategies to overcome the computational costs due to evaluations of multibody interactions by additional …
Mathematical Strategies In The Coarse-Graining Of Extensive Systems: Error Quantification And Adaptivity, Ma Katsoulakis, P Plechac, L Rey-Bellet, Dk Tsagkarogiannis
Mathematical Strategies In The Coarse-Graining Of Extensive Systems: Error Quantification And Adaptivity, Ma Katsoulakis, P Plechac, L Rey-Bellet, Dk Tsagkarogiannis
Luc Rey-Bellet
In this paper we continue our study of coarse-graining schemes for stochastic many-body microscopic models started in Katsoulakis et al. [M. Katsoulakis, A. Majda, D. Vlachos, Coarse-grained stochastic processes for microscopic lattice systems, Proc. Natl. Acad. Sci. 100 (2003) 782–782, M.A. Katsoulakis, L. Rey-Bellet, P. Plecháč, D. Tsagkarogiannis, Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems, M2AN Math. Model. Numer. Anal., in press], focusing on equilibrium stochastic lattice systems. Using cluster expansion techniques we expand the exact coarse-grained Hamiltonian around a first approximation and derive higher accuracy schemes by including more terms in the expansion. The accuracy …
Large Deviations In Non-Uniformly Hyperbolic Dynamical Systems, L Rey-Bellet, Ls Young
Large Deviations In Non-Uniformly Hyperbolic Dynamical Systems, L Rey-Bellet, Ls Young
Luc Rey-Bellet
We prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limit theorems are derived is the analyticity of logarithmic moment generating functions. Among the classes of dynamical systems to which our results apply are piecewise hyperbolic diffeomorphisms, dispersing billiards including Lorentz gases, and strange attractors of rank one including Hénon-type attractors.