Occupation probabilities and fluctuations in the asymmetric simple inclusion process.
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.
Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv 69978, Israel and Department of Systems Biology, Harvard University, Boston, Massachusetts 02115, USA.
Shlomi
S
Reuveni
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
Ori
O
Hirschberg
Department of Technology Management, Holon Institute of Technology, Holon 58102, Israel.
Iddo
I
Eliazar
Department of Statistics and Operations Research, Tel-Aviv University, Tel-Aviv 69978, Israel.
Uri
U
Yechiali