%0 Journal Article %T Tau-function of discrete isomonodromy transformations and probability %A D. Arinkin %A A. Borodin %J Mathematics %D 2007 %I arXiv %R 10.1112/S0010437X08003862 %X 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. %U http://arxiv.org/abs/0706.3073v1