An asymptotic result for brownian polymers
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 1, p. 29-46

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.

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.

DOI : https://doi.org/10.1214/07-AIHP113
Classification:  60F15,  60K35
Keywords: self-interacting diffusions, repulsive interaction, superdiffusive process, almost sure law of large numbers
@article{AIHPB_2008__44_1_29_0,
     author = {Mountford, Thomas and Tarr\`es, Pierre},
     title = {An asymptotic result for brownian polymers},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {44},
     number = {1},
     year = {2008},
     pages = {29-46},
     doi = {10.1214/07-AIHP113},
     zbl = {1175.60084},
     mrnumber = {2451570},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2008__44_1_29_0}
}
Mountford, Thomas; Tarrès, Pierre. An asymptotic result for brownian polymers. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 1, pp. 29-46. doi : 10.1214/07-AIHP113. http://www.numdam.org/item/AIHPB_2008__44_1_29_0/

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