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
N1 - Israel Science Foundation (ISF); Minerva Foundation; Federal German Ministry for Education and Research; James S. McDonnell FoundationWe gratefully acknowledge Amir Bar, Or Cohen, and David Mukamel for fruitful discussions. The support of the Israel Science Foundation (ISF) and of the Minerva Foundation with funding from the Federal German Ministry for Education and Research is gratefully acknowledged. Shlomi Reuveni gratefully acknowledges support from the James S. McDonnell Foundation via its postdoctoral fellowship in studying complex systems.
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 - https://www.scopus.com/pages/publications/84899706972
U2 - 10.1103/PhysRevE.89.042109
DO - 10.1103/PhysRevE.89.042109
M3 - Article
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 -