The Loday-Quillen-Tsygan (LQT) map relates the cyclic cohomology of an algebra to the Lie algebra cohomology of the NxN matrices in that algebra. We show that the LQT map respects a BV quantization, and then use the quantization to explicitly compute certain aspects of correlation functions of random matrices. This is joint work with Alastair Hamilton, Gregory Ginot, and Owen Gwilliam.