Rate of convergence for polymers in a weak disorder
Résumé
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.
Domaines
Probabilités [math.PR]
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comets_liu_polymers_speed_of_conv_2017_05_JMAA_definitive.pdf (421.07 Ko)
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