Complementary information on the random walk with that supplied with the Green’s function is contained in path PDFs. This is evident, when constructing approximations for Green’s functions, in which path PDFs are the building blocks in the analysis. Also, analytical properties of the Green’s function are clarified only in path PDF analysis. Here, presented is the recursion relation for w i j ( τ τ , 2 n + γ γ i j ; L ) in the length n of path PDFs for any fixed value of L. The recursion relation is linear in path PDFs with the h ¯ ¯ ( s , i ; L ) s in Eq. (5) serving as the n independent coefficients, and is of order [ L / 2]: