Tails of the endpoint distribution of directed polymers
Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 1, p. 1-17

We prove that the random variable 𝒯=arg max t {𝒜 2 (t)-t 2 }, where 𝒜 2 is the Airy 2 process, has tails which decay like e -ct 3 . The distribution of 𝒯 is a universal distribution which governs the rescaled endpoint of directed polymers in 1+1 dimensions for large time or temperature.

Nous prouvons qu’une variable aléatoire 𝒯=arg max t {𝒜 2 (t)-t 2 }, où 𝒜 2 est un processus Airy 2 a une queue qui décroît comme e -ct 3 . La distribution de 𝒯 est une distribution universelle qui gouverne la position du point final d’un polymère dirigé en dimension 1+1 à temps grand ou à grande température.

DOI : https://doi.org/10.1214/12-AIHP525
Classification:  60K35,  82C23
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},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {1},
     year = {2015},
     pages = {1-17},
     doi = {10.1214/12-AIHP525},
     zbl = {06412895},
     mrnumber = {3300961},
     language = {en},
     url = {http://www.numdam.org/item/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/item/AIHPB_2015__51_1_1_0/

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