Exact Calculation of the Large Deviation Function for k-nary Coalescence

We study probabilities of rare events in the general coalescence process, $$kA\rightarrow \ell A$$ , where $$k>\ell $$ . For arbitrary $$k, \ell $$ , by rewriting these probabilities in terms of an effective action, we derive the large deviation function describing the probability of finding N particles at time t, when starting with M particles initially. Additionally, the most probable trajectory corresponding to a fixed rare event is derived.