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The Asymmetric Simple Inclusion Process (ASIP), a lattice-gas model ofunidirectional transport and aggregation, was recently proposed as an`inclusion' counterpart of the Asymmetric Simple Exclusion Process (ASEP). Inthis paper we present an exact closed-form expression for the probability thata given number of particles occupies a given set of consecutive lattice sites.Our results are expressed in terms of the entries of Catalan's trapezoids ---number arrays which generalize Catalan's numbers and Catalan's triangle. Wefurther prove that the ASIP is asymptotically governed by: (i) an inversesquare root law of occupation; (ii) a square root law of fluctuation; and (iii)a Rayleigh law for the distribution of inter-exit times. The universality ofthese results is discussed.

Occupation Probabilities and Fluctuations in the Asymmetric Simple Inclusion Process