离散等距变换的Tau函数与概率
Tau-function of discrete isomonodromy transformations and probability
摘要：
我们引入了有理d-联络的τ-函数及其等价变换。我们证明了在连续极限下我们的τ函数与Jimbo-Miwa-Ueno τ函数一致，计算了导致差分Painleve V和差分Painleve VI方程的等势变换的τ函数，并证明了一类离散随机矩阵型模型的间隙概率可以看作是相关d-连接的τ函数.
英文摘要：
We introduce the tau-function of a rational d-connection and its isomonodromy transformations. We show that in a continuous limit our tau-function agrees with the Jimbo-Miwa-Ueno tau-function, compute the tau-function for the isomonodromy transformations leading to difference Painleve V and difference Painleve VI equations, and prove that the gap probability for a wide class of discrete random matrix type models can be viewed as the tau-function for an associated d-connection.
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