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We derive a generic expression for the generating function (GF) of theparticle-number probability distribution (PNPD) for a simple reaction diffusionmodel that belongs to the directed percolation universality class. Startingwith a single particle on a lattice, we show that the GF of the PNPD can bewritten as an infinite series of cumulants taken at zero momentum. This seriescan be summed up into a complete form at the level of a mean-fieldapproximation. Using the renormalization group techniques, we determinelogarithmic corrections for the GF at the upper critical dimension. We alsofind the critical scaling form for the PNPD and check its universalitynumerically in one dimension. The critical scaling function is found to beuniversal up to two non-universal metric factors.Comment: (v1,2) 8 pages, 5 figures; one-loop calculation corrected in response  to criticism received from Hans-Karl Janssen, (v3) content as publishe

Generating function for particle-number probability distribution in directed percolation