We prove that the random variable , where is the process, has tails which decay like . The distribution of is a universal distribution which governs the rescaled endpoint of directed polymers in dimensions for large time or temperature.
Nous prouvons qu’une variable aléatoire , où est un processus a une queue qui décroît comme . La distribution de est une distribution universelle qui gouverne la position du point final d’un polymère dirigé en dimension à temps grand ou à grande température.
Keywords: directed random polymers, Kardar–Parisi–Zhang universality class
@article{AIHPB_2015__51_1_1_0, author = {Quastel, Jeremy and Remenik, Daniel}, title = {Tails of the endpoint distribution of directed polymers}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {1--17}, publisher = {Gauthier-Villars}, volume = {51}, number = {1}, year = {2015}, doi = {10.1214/12-AIHP525}, mrnumber = {3300961}, zbl = {06412895}, language = {en}, url = {http://www.numdam.org/articles/10.1214/12-AIHP525/} }
TY - JOUR AU - Quastel, Jeremy AU - Remenik, Daniel TI - Tails of the endpoint distribution of directed polymers JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2015 SP - 1 EP - 17 VL - 51 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/12-AIHP525/ DO - 10.1214/12-AIHP525 LA - en ID - AIHPB_2015__51_1_1_0 ER -
%0 Journal Article %A Quastel, Jeremy %A Remenik, Daniel %T Tails of the endpoint distribution of directed polymers %J Annales de l'I.H.P. Probabilités et statistiques %D 2015 %P 1-17 %V 51 %N 1 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/12-AIHP525/ %R 10.1214/12-AIHP525 %G en %F AIHPB_2015__51_1_1_0
Quastel, Jeremy; Remenik, Daniel. Tails of the endpoint distribution of directed polymers. Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 1, pp. 1-17. doi : 10.1214/12-AIHP525. http://www.numdam.org/articles/10.1214/12-AIHP525/
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