Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Large scale behavior of semiflexible heteropolymers

Francesco Caravenna, Giambattista Giacomin, and Massimiliano Gubinelli

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Abstract

We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a Brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative Fourier analysis, we establish the Brownian character of the model on large scales and we obtain an expression for the diffusion constant. We moreover give conditions yielding quantitative mixing properties.

Résumé

On considère un modèle discret pour un polymère semi-flexible et hétérogène. Le bruit thermique et le caractère hétérogène du polymère (le désordre) sont modélisés en termes de rotations aléatoires. Nous nous concentrons sur le régime de désordre gélé, c’est-à-dire, l’analyse est effectuée pour une réalisation fixée du désordre. Les modèles semi-flexibles diffèrent sensiblement des marches aléatoires à petite échelle, mais à grande échelle un comportement brownien apparaît. En exploitant des techniques de calcul tensoriel et d’analyse de Fourier non-commutative, nous établissons le caractère brownien du modèle à grande échelle et nous obtenons une expression pour la constante de diffusion. Nous donnons aussi des conditions qui entraînent des propriétés quantitatives de mélange.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist. Volume 46, Number 1 (2010), 97-118.

Dates
First available in Project Euclid: 1 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1267454110

Digital Object Identifier
doi:10.1214/08-AIHP310

Mathematical Reviews number (MathSciNet)
MR2641772

Zentralblatt MATH identifier
1192.82041

Subjects
Primary: 60K37: Processes in random environments 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 60F05: Central limit and other weak theorems 43A75: Analysis on specific compact groups

Keywords
Heteropolymer Semiflexible chain Disorder Persistence length Large scale limit Tensor analysis Non-commutative Fourier analysis

Citation

Caravenna, Francesco; Giacomin, Giambattista; Gubinelli, Massimiliano. Large scale behavior of semiflexible heteropolymers. Ann. Inst. H. Poincaré Probab. Statist. 46 (2010), no. 1, 97--118. doi:10.1214/08-AIHP310. https://projecteuclid.org/euclid.aihp/1267454110


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