Related papers: Intertwining Markov Processes via Matrix Product O…

In this paper we continue studying of matrix $n\times n$ linear differential intertwining operators. The problems of minimization and of reducibility of matrix intertwining operators are considered and criterions of weak minimizability and…

We introduce a spin ladder with discrete symmetries designed to emulate a two-dimensional spin-1/2 boson system at half-filling. Using global properties, such as the structure of topological defects, we establish a correspondence between…

In this article we consider the Markovian products of invertible (not necessarily positive) matrices chosen from a strongly irreducible, contracting, finite set of matrices. We construct Markovian transfer operators and prove the spectral…

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…

Matrix coordinate transformations are defined as substitution operators without requiring an ordering prescription or an inclusion function from the Abelian coordinate transformations. We construct transforming objects mimicking most of the…

We study one-dimensional lattice systems with pair-wise interactions of infinite range. We show projective convergence of Markov measures to the unique equilibrium state. For this purpose we impose a slightly stronger condition than…

Let $({\mathcal X}, d, \mu)$ be a metric measure space and satisfy the so-called upper doubling condition and the geometrically doubling condition. In this paper, the authors establish an interpolation result that a sublinear operator which…

We study invariant boundary conditions for one dimensional discrete Gaussian Markov processes, basic toy models of spatial Markov processes in statistical mechanics. More precisely, we give a decomposition of boundary objects in a non…

For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker-Planck dynamics involving an arbitrary force $F(x)$ and an arbitrary diffusion coefficient $D(x)$,…

We start from the observation that, anytime two Markov generators share an eigenvalue, the function constructed from the product of the two eigenfunctions associated to this common eigenvalue is a duality function. We push further this…

We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…

In this paper we show how questions about operator algebras constructed from stochastic matrices motivate new results in the study of harmonic functions on Markov chains. More precisely, we characterize coincidence of conditional…

Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…

Infinite sets of inequalities which generalize all the known inequalities that can be used in the majorization step of the Approximating Hamiltonian method are derived. They provide upper bounds on the difference between the quadratic…

We consider optimal control problems for a wide class of bilateral obstacle problems where the control appears in a possibly nonlinear source term. The non-differentiability of the solution operator poses the main challenge for the…

We prove exponential decay of pair correlations for 1D stationary point processes when spacings satisfy a Markov condition, geometric ergodicity, and a condition on exponential moments. The conditions are phrased for stationary sequences of…

It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

(I.) We consider generalizations of an iterated function system and the associated Markov operators. A Markov operator, defined on the space of (deficient) topological measures on a locally compact space, is an infinite convex linear…

We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall…