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.

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: 10.1214/12-AIHP525
Classification: 60K35, 82C23
Keywords: directed random polymers, Kardar–Parisi–Zhang universality class
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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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