Q−orthogonal dualities for asymmetric particle systems

We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP(q, θ), asymmetric exclusion process, with a repulsive interaction, allowing up to θ ∈ N particles in each site, and the ASIP(q, θ), θ ∈ R⁺, asymmetric inclusion process, that is its attractive...

Higher order fluctuation fields and orthogonal duality polynomials

Inspired by the works in [2] and [11] we introduce what we call k-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This type of duality provides us with a setting in which we are able to interpret these fields as some type of...

Condensation of SIP Particles and Sticky Brownian Motion

We study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite...

Exact formulas for two interacting particles and applications in particle systems with duality

We consider two particles performing continuous-time nearest neighbor random walk on Z and interacting with each other when they are at neighboring positions. The interaction is either repulsive (partial exclusion process) or attractive (inclusion process). We provide an exact formula for the Laplace-Fourier transform of the transition...

Orthogonal Dualities of Markov Processes and Unitary Symmetries

We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that orthogonal self-dualities arise from unitary symmetries of the Markov generator. For these symmetries we provide two equivalent expressions that are related...

Stationary States in Infinite Volume with Non-zero Current

We study the Ginzburg–Landau stochastic models in infinite domains with some special geometry and prove that without the help of external forces there are stationary measures with non-zero current in three or more dimensions.

Quantitative Boltzmann–Gibbs Principles via Orthogonal Polynomial Duality

We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann–Gibbs principle. In the...

Asymmetric Stochastic Transport Models with Uq(su(1,1)) Symmetry

By using the algebraic construction outlined in Carinci et al. (arXiv:?1407.?3367, 2014), we introduce several Markov processes related to the Uq(su(1,1)) quantum Lie algebra. These processes serve as asymmetric transport models and their algebraic structure easily allows to deduce duality properties of the systems. The results include: (a) the...

A generalized asymmetric exclusion process with Uq(sl2) stochastic duality

We study a new process, which we call ASEP(q, j ), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by q ? (0, 1) and where at most 2 j ? N particles per site are allowed. The process is constructed from a (2 j + 1)-dimensional representation of a quantum Hamiltonian with Uq (sl2) invariance by...

A generalized asymmetric exclusion process with Uq(sl2) stochastic duality

We study a new process, which we call ASEP(q, j), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by q ∈ (0, 1) and where at most 2 j ∈ N particles per site are allowed. The process is constructed from a (2 j + 1)-dimensional representation of a quantum Hamiltonian with Uq (sl2) invariance by...