An asymptotic result for brownian polymers

Mountford, Thomas; Tarrès, Pierre

doi:10.1214/07-AIHP113

Mountford, Thomas ; Tarrès, Pierre

Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 1, pp. 29-46.

Résumé
Abstract

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 $X_{t}$ (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.

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.

MR Zbl | 2 citations dans Numdam

DOI : 10.1214/07-AIHP113

Classification : 60F15, 60K35
Mots-clés : self-interacting diffusions, repulsive interaction, superdiffusive process, almost sure law of large numbers

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Mountford, Thomas; Tarrès, Pierre. An asymptotic result for brownian polymers. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 1, pp. 29-46. doi : 10.1214/07-AIHP113. http://www.numdam.org/articles/10.1214/07-AIHP113/

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