Exact calculation of the large deviation function for $k$-nary coalescence

Abstract

We study probabilities of rare events in the general coalescence process, $kA\to \ell A$, 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.

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