  We show existence of the weak large deviation principle, with a convex rate
function, for the renormalized distance from the starting point of irreducible
random walks on relatively hyperbolic groups. Under the assumption of
finiteness of exponential moments, the full large deviation principle holds,
and the rate function governing it can be expressed as the Fenchel-Legendre
transform of the limiting logarithmic moment generating function of the
sequence of renormalized distances.
