# Rate of convergence for polymers in a weak disorder

* Corresponding author
Abstract : We consider directed polymers in random environment on the lattice $Z^d$ at small inverse temperature and dimension $d \geq 3$. Then, the normalized partition function $W_n$ is a regular martingale with limit W. We prove that $n^{(d−2)/4} (W_n−W)/W_n$ converges in distribution to a Gaussian law. Both the polynomial rate of convergence and the scaling with the martingale $W_n$ are different from those for polymers on trees.
Document type :
Journal articles
Domain :

Cited literature [31 references]

https://hal.archives-ouvertes.fr/hal-01705859
Contributor : Quansheng Liu <>
Submitted on : Friday, February 9, 2018 - 9:23:20 PM
Last modification on : Friday, March 27, 2020 - 3:54:59 AM
Document(s) archivé(s) le : Friday, May 4, 2018 - 12:37:35 AM

### File

comets_liu_polymers_speed_of_c...
Files produced by the author(s)

### Citation

Francis Comets, Quansheng Liu. Rate of convergence for polymers in a weak disorder. Journal of Mathematical Analysis and Applications, Elsevier, 2017, 455 (1), pp.312 - 335. ⟨10.1016/j.jmaa.2017.05.043⟩. ⟨hal-01705859⟩

Record views