W i j ( t ; L ) is the PDF of reaching state i exactly at time t when starting at state j exactly at time 0. This is the path PDF in time that is built from all paths with 2 n + γ γ i j transitions that connect states j with i. Two different path types contribute to w i j ( τ τ , 2 n + γ γ i j ; L ) : paths made of the same states appearing in different orders and different paths of the same length of 2 n + γ γ i j transitions. Path PDFs for translation invariant chains are mono-peaked. Path PDF for translation invariant chains mostly contribute to the Green's function in the vicinity of its peak, but this behavior is believed to characterize heterogeneous chains as well.