  We introduce a simple yet powerful calculational tool useful in calculating
averages of ratios and products of characteristic polynomials. The method is
based on Dyson Brownian motion and Grassmann integration formula for
determinants. It is intended as an alternative to other RMT techniques
applicable to general gaussian measures. Resulting formulas are exact for
finite matrix size N and form integral representations convenient for large N
asymptotics. Quantities obtained by the method can be interpreted as averages
over matrix models with an external source. We provide several explicit and
novel calculations showing a range of applications.
