The Distribution of Iras Galaxies on Linear and Non-linear Scales

We analyze the galaxy distribution functions for voids and counts-in-cells using the IRAS catalog. Angular diameter scales, the largest probed to date, range from 0:5 to 30 , corresponding to linear diameters < 40h ?1 Mpc. The analysis develops a new technique which has no free parameters. On all scales, the results agree closely with the predictions of simple gravitational galaxy clustering. The value of b pattern for the IRAS galaxies at a cell diameter of 30 is 0:62 0:03. It is nearly independent of scale for angular diameters > 20. We also develop a new method for using the projected distribution functions to estimate the average amplitude, ?, and scale, r neg , where the spatial two-point galaxy correlation function, 2 , becomes negative. This technique is sensitive to the negative range of 2 and is independent of the peculiar velocity eeects which make measurements of the spatial correlation function uncertain on some scales. It shows that a large class of CDM-related models, with linear biasing, appears to be inconsistent with the IRAS distribution. We discuss some implications for the selection of the IRAS galaxies, the scale invariance of higher order moments of the IRAS distribution function, and the evidence that initial conditions for galaxy clustering were Gaussian. subject headings: cosmology: theory { galaxies: clustering { infrared: galaxies { large-scale structure of universe { methods: numerical