Related papers: Inhomogeneous discrete-time exclusion processes

In this article we study the causality of non-homogeneous linear singular discrete time systems whose coefficients are square constant matrices. By assuming that the input vector changes only at equally space sampling instants we provide…

We give a complete classification of integrable Markovian boundary conditions for the asymmetric simple exclusion process with two species (or classes) of particles. Some of these boundary conditions lead to non-vanishing particle currents…

Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between…

The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time dependent parameters such as periodic external forces or slowly fluctuating barrier…

We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process…

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

We study the long time asymptotics of the relaxation dynamics of the totally asymmetric simple exclusion process on a ring. Evaluating the asymptotic amplitudes of the local currents by the algebraic Bethe ansatz method, we find the…

We propose an analytic approach for the steady-state dynamics of Markov processes on locally tree-like graphs. It is based on time-translation invariant probability distributions for edge trajectories, which we encode in terms of infinite…

Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains,…

We consider a finite state discrete time process X. Without loss of generality the finite state space can be identified with the set of unit vectors {e1, e2, . . . , eN} with ei = (0, . . . , 0, 1, 0, . . . , 0)0 2 RN. For a Markov chain…

A simple relation between inhomogeneous transfer matrices and boundary quantum KZ equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus…

The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…

This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

Consider a continuous time particle system $\eta^t=(\eta^t(k),k\in \mathbb{L})$, indexed by a lattice $\mathbb{L}$ which will be either $\mathbb{Z}$, $\mathbb{Z}/n\mathbb{Z}$, a segment $\{1,\cdots, n\}$, or $\mathbb{Z}^d$, and taking its…

Markov-modulated Brownian motion is a popular tool to model continuous-time phenomena in a stochastic context. The main quantity of interest is the invariant density, which satisfies a differential equation associated with the quadratic…

We consider the case of an integrable quantum spin chain with ``soliton non-preserving'' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…

Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…