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 (correspondant à l’emplacement de l’extrémité du polymère au temps ) 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 (corresponding to the location of the end of the polymer at time ) for a particular type of repelling interaction function without compact support.
Mots clés : 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}, pages = {29--46}, publisher = {Gauthier-Villars}, volume = {44}, number = {1}, year = {2008}, doi = {10.1214/07-AIHP113}, mrnumber = {2451570}, zbl = {1175.60084}, language = {en}, url = {http://www.numdam.org/articles/10.1214/07-AIHP113/} }
TY - JOUR AU - Mountford, Thomas AU - Tarrès, Pierre TI - An asymptotic result for brownian polymers JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2008 SP - 29 EP - 46 VL - 44 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/07-AIHP113/ DO - 10.1214/07-AIHP113 LA - en ID - AIHPB_2008__44_1_29_0 ER -
%0 Journal Article %A Mountford, Thomas %A Tarrès, Pierre %T An asymptotic result for brownian polymers %J Annales de l'I.H.P. Probabilités et statistiques %D 2008 %P 29-46 %V 44 %N 1 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/07-AIHP113/ %R 10.1214/07-AIHP113 %G en %F 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, 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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