Rate of convergence for polymers in a weak disorder

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Comets, Francis¹  Liu, Quansheng² 

[1] Univ Paris Diderot Paris 7, Math, Case 7012, F-75205 Paris 13, France

[2] Univ Bretagne Sud, LMBA, UMR 6205, F-56000 Vannes, France

关键词: Directed polymers;    Random environment;    Weak disorder;    Rate of convergence;    Central limit theorem for martingales;    Stable and mixing convergence;   

DOI  :  10.1016/j.jmaa.2017.05.043

来源: Elsevier

【 摘 要 】

We consider directed polymers in random environment on the lattice Z(d) at small inverse temperature and dimension d >= 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free