论文标题
带有一般参数和斜率的log-gamma聚合物自由能的波动
Fluctuations of the log-gamma polymer free energy with general parameters and slopes
论文作者
论文摘要
我们证明，晶格点$（1,1）$和$（m，n）$之间的log-gamma聚合物的自由能收敛到$ m^{1/3} $缩放中的gue tracy-widom分布，但前提是$ n/m $保持偏离零和无限。我们证明了该模型具有任何形状参数$θ> 0 $的逆伽玛的权重，并且在这种情况下为自由能的上尾部建立了适度的偏差估计值。最后，我们考虑了一个非I.I.D.设置有限的许多行和列上的权重具有不同的参数，我们表明，当这些参数严格地缩放时，限制自由能波动受到Baik-ben唤醒的唤醒随机分布的概括的控制，并具有两组参数。
We prove that the free energy of the log-gamma polymer between lattice points $(1,1)$ and $(M,N)$ converges to the GUE Tracy-Widom distribution in the $M^{1/3}$ scaling, provided that $N/M$ remains bounded away from zero and infinity. We prove this result for the model with inverse gamma weights of any shape parameter $θ>0$ and furthermore establish a moderate deviation estimate for the upper tail of the free energy in this case. Finally, we consider a non i.i.d. setting where the weights on finitely many rows and columns have different parameters, and we show that when these parameters are critically scaled the limiting free energy fluctuations are governed by a generalization of the Baik-Ben Arous-Péché distribution from spiked random matrices with two sets of parameters.
