pfdietz is correct. The key thing is that divergences always multiply, leading to an exponential dependence on number of scattering events. There isn't a transi

pfdietz is correct. The key thing is that divergences always multiply, leading to an exponential dependence on number of scattering events. There isn't a transition between a linear and an exponential dependence. I think where you're getting confused is that an exponential can be initially approximated by a linear function (i.e. exp(x) ~= 1 + x), but that doesn't mean that the process is linear. The dominance of the exponential growth is also why the tidal correction, as massive as it seems, gets swamped and ends up not mattering much. -- Raghu Parthasarathy