An asymptotic result for Brownian polymers

Abstract

We consider a model of the shape of a growing polymer introduced by Durrett and Rogers (Probab. Theory Related Fields 92 (1992) 337--349). We prove their conjecture about the asymptotic behavior of the underlying continuous process $X_t$ (corresponding to the location of the end of the polymer at time $t$) for a particular type of repelling interaction function without compact support.

Published in at http://dx.doi.org/10.1214/07-AIHP113 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Some particular self-interacting diffusions: Ergodic behaviour and almost sure convergence
• Diffusive limits for "true" (or myopic) self-avoiding random walks and self-repellent Brownian polymers in d >= 3
• Self-repelling random walk with directed edges on Z
• Self-repelling diffusions on a Riemannian manifold
• Stability of the Greedy Algorithm on the Circle
• Random walk with barycentric self-interaction
• Random walks avoiding their convex hull with a finite memory
• The ODE method for some self-interacting diffusions on non-compact spaces