In a companion paper, a quenched large deviation principle (LDP) has been established
for the empirical process of words obtained by cutting an i.i.d. sequence of letters into words according to a renewal process. We apply this LDP to prove that the radius of convergence of the moment generating function of the collision local time of two strongly transient random walks on Zd, d = 1, strictly increases when we condition on one of the random walks, both in discrete time and in continuous time. We conjecture that the same holds for two transient but not strongly transient random walks. The presence of these gaps implies the existence of an intermediate phase for the long-time behaviour of a class of coupled branching processes, interacting diffusions, respectively, directed polymers in random environments.
|Place of Publication||Eindhoven|
|Number of pages||16|
|Publication status||Published - 2008|