Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations

  title={Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations},
  author={Simone Floreani and Frank Redig and F. Sau},
  journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n… 

Figures from this paper

Exact solution of an integrable non-equilibrium particle system
We consider the boundary-driven interacting particle systems introduced in [FGK20a] related to the open non-compact Heisenberg model in one dimension. We show that a finite chain of N sites connected
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
Boundary driven Markov gas: duality and scaling limits
Inspired by the recent work of Bertini and Posta [3], who introduced the boundary driven Brownian gas on [0, 1], we study boundary driven systems of independent particles in a general setting,
Scaling Limits of Random Walks, Harmonic Profiles, and Stationary Non-Equilibrium States in Lipschitz Domains
We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Ω, with both fast and slow boundary. For the random walks on Ω dual to SEP/SIP we establish:
Duality in quantum transport models
We develop the `duality approach', that has been extensively studied for classical models of transport, for quantum systems in contact with a thermal `Lindbladian' bath. The method provides (a) a
Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics
We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the
Classification of Stationary distributions for the stochastic vertex models
. In this paper, we study the stationary distribution for the stochastic vertex models. Our main focus is the stochastic six vertex (S6V) model. We show that the extreme stationary distributions of
of the Bernoulli Society for Mathematical Statistics and Probability Volume Twenty Eight Number Two May 2022
A list of forthcoming papers can be found online at http://www.bernoullisociety.org/index. php/publications/bernoulli-journal/bernoulli-journal-papers CONTENTS 713 BELLEC, P.C. and ZHANG, C.-H.
Switching Interacting Particle Systems: Scaling Limits, Uphill Diffusion and Boundary Layer
This paper considers three classes of interacting particle systems on $${{\mathbb {Z}}}$$ Z : independent random walks, the exclusion process, and the inclusion process. Particles are allowed to
Intertwining and Duality for Consistent Markov Processes
In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to


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
Stochastic Duality and Orthogonal Polynomials
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which
Duality for Stochastic Models of Transport
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model
Entropy of Open Lattice Systems
We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in
Hydrodynamics for the partial exclusion process in random environment
Stochastic interacting particle systems out of equilibrium
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are
Exact solution of a 1d asymmetric exclusion model using a matrix formulation
Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be
Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems
Motivated by the recent preprint [arXiv:2004.08412] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher order fields. Then, by considering the
Local Equilibrium in Inhomogeneous Stochastic Models of Heat Transport
We extend the duality of Kipnis et al. (J Stat Phys 27:65–74, 1982) to inhomogeneous lattice gas systems where either the components have different degrees of freedom or the rate of interaction