  We derive analytic expressions for force propagation in packings of
frictionless discs with a narrow distribution of disc sizes, by expanding to
first order about the known ordered solution. The distribution of contact
forces P(f) is found to be narrow at the upper surface, and broaden at a rate
that varies with depth, being superdiffusive near the surface until crossing
over to a subdiffusive regime near the fixed base. Furthermore, the response to
an isolated load propagates along the edge of a `cone,' as in the ordered case,
but fluctuates under ensemble averaging by an amount that depends purely on
height, not on the lateral position. Finally, we comment on ways in which the
analytical framework presented here could be extended to a wider range of
granular packings.
