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We study the free energy fluctuations for a mixture of directed polymers,which was first introduced by Borodin et al.(2015)to investigate the limiting distribution of a stationary Kardar-Parisi-Zhang(KPZ)equation.The main results consist of both the law of large numbers and the asymptotic fluctuation for the free energy as the model size tends to infinity.In particular,we find the explicit values(which may depend on model parameters)of normalizing constants in the fluctuation.This shows that such a mixture model is in the KPZ university class.
We study the free energy fluctuations for a mixture of directed polymers, which was first introduced by Borodin et al. (2015) to investigate the limiting distribution of a stationary Kardar-Parisi-Zhang (KPZ) equation. The main results consist of both the law of large numbers and the asymptotic fluctuation for the free energy as the model size tends to infinity.In particular, we find the explicit values (which may depend on model parameters) of normalizing constants in the fluctuation. This shows that such a mixture model is in the KPZ university class.