Measurement of the conductance distribution function at a quantum Hall transition

We study experimentally the reproducible conductance fluctuations between the quantum Hall plateaus in the conductance of two-terminal submicrometer silicon MOSFET's. For the dramatic fluctuations at the insulator-to-first-plateau transition we find a conductance distribution that is approximately uniform between zero and $\frac{e^2}{h}$. We point out that this is consistent with the prediction of random $S$-matrix theory for a conductor with single-channel leads in a magnetic field.