Limit laws for the asymmetric inclusion process

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Complex Systems

Background:

• The Asymmetric Inclusion Process (ASIP) is a unidirectional lattice-gas model.
• It serves as a 'Bosonic' counterpart to the 'Fermionic' asymmetric exclusion process.
• Exact computation of the ASIP's steady-state probability generating function (PGF) is limited to small lattices.

Purpose of the Study:

• To analytically investigate the asymptotic statistical behavior of the ASIP.
• To derive closed-form stochastic limit laws for key observables in large ASIP lattices.
• To provide a theoretical framework complementing Monte Carlo simulations.

Main Methods:

• Analysis of three limiting regimes: heavy-traffic, large-system, and balanced-system.
• Derivation of analytical, closed-form stochastic limit laws.
• Comparison with numerical simulations to validate approximations.

Main Results:

• Obtained analytical, closed-form stochastic limit laws for traversal time, overall load, busy period, first occupied site, and draining time.
• Demonstrated the applicability of these laws as approximations for large ASIP lattices.
• Provided a detailed limit-laws perspective on ASIP's statistical phenomena.

Conclusions:

• The derived limit laws offer a powerful analytical tool for understanding large-scale ASIP behavior.
• These findings bridge the gap between exact solutions for small systems and simulation-based studies of large systems.
• The study enhances the theoretical understanding of non-equilibrium lattice models.