We consider the bipartite Sherrington–Kirkpatrick model in which the variance of disorders depends only on the species the particles belong to. By using the stochastic calculus method, we obtain the fluctuation result for the partition function in the absence of an external field. When the external field is nonzero, the central limit theorem for the free energy is also derived through a different stochastic calculus approach. It turns out that the corresponding convergence rates are not the same in those two cases.

中文翻译：

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二分谢林顿-柯克帕特里克模型的波动

我们考虑二分 Sherrington-Kirkpatrick 模型，其中紊乱的方差仅取决于粒子所属的物种。通过使用随机微积分方法，我们得到了在没有外场的情况下配分函数的涨落结果。当外场不为零时，自由能的中心极限定理也是通过不同的随机微积分方法推导出来的。事实证明，这两种情况下相应的收敛速度并不相同。