TY - JOUR

T1 - Occupation probabilities and fluctuations in the asymmetric simple inclusion process

AU - Reuveni, Shlomi

AU - Hirschberg, Ori

AU - Eliazar, Iddo

AU - Yechiali, Uri

PY - 2014/4/4

Y1 - 2014/4/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84899706972&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.89.042109

DO - 10.1103/PhysRevE.89.042109

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AN - SCOPUS:84899706972

SN - 1539-3755

VL - 89

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 4

M1 - 042109

ER -