Occupation probabilities and fluctuations in the asymmetric simple inclusion process

Shlomi Reuveni, Ori Hirschberg, Iddo Eliazar, Uri Yechiali

Research output: Contribution to journalArticlepeer-review


The asymmetric simple inclusion process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an "inclusion" counterpart of the asymmetric simple exclusion process. In this paper we present an exact closed-form expression for the probability that a 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. We further prove that the ASIP is asymptotically governed by the following: (i) an inverse square-root law of occupation, (ii) a square-root law of fluctuation, and (iii) a Rayleigh law for the distribution of interexit times. The universality of these results is discussed.

Original languageEnglish
Article number042109
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
StatePublished - 4 Apr 2014


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