Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

An asymptotic result for Brownian polymers

Thomas Mountford and Pierre Tarrès

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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 Xt (corresponding to the location of the end of the polymer at time t) for a particular type of repelling interaction function without compact support.

Résumé

Nous considérons un modèle de formation de polymères introduit par Durrett et Rogers (Probab. Theory Related Fields 92 (1992) 337–349). Nous prouvons leur conjecture sur le comportement asymptotique du processus continu associé Xt (correspondant à l’emplacement de l’extrémité du polymère au temps t) pour un type particulier de fonction d’interaction répulsive à support non compact.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 1 (2008), 29-46.

Dates
First available in Project Euclid: 25 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1203969867

Digital Object Identifier
doi:10.1214/07-AIHP113

Mathematical Reviews number (MathSciNet)
MR2451570

Zentralblatt MATH identifier
1175.60084

Subjects
Primary: 60F15: Strong theorems 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Self-interacting diffusions Repulsive interaction Superdiffusive process Almost sure law of large numbers

Citation

Mountford, Thomas; Tarrès, Pierre. An asymptotic result for Brownian polymers. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 1, 29--46. doi:10.1214/07-AIHP113. https://projecteuclid.org/euclid.aihp/1203969867


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