Related papers: Matrix product formula for $U_q(A^{(1)}_2)$-zero r…
This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
Measure-free discrete time stochastic processes in Riesz spaces were formulated and studied by Kuo, Labuschagne and Watson. Aspects relating martingales, stopping times, convergence of these processes as well as various decomposition were…
We prove a intertwining relation (or Markov duality) between the $(q,\mu,\nu)$-Boson process and $(q,\mu,\nu)$-TASEP, two discrete time Markov chains introduced by Povolotsky. Using this and a variant of the coordinate Bethe ansatz we…
We propose a dynamical matrix product ansatz describing the stochastic dynamics of two species of particles with excluded-volume interaction and the quantum mechanics of the associated quantum spin chains respectively. Analyzing consistency…
Markov categories are a recent category-theoretic approach to the foundations of probability and statistics. Here we develop this approach further by treating infinite products and the Kolmogorov extension theorem. This is relevant for all…
We construct quadratic stochastic processes (QSP) (also known as Markov processes of cubic matrices) in continuous and discrete times. These are dynamical systems given by (a fixed type, called $\sigma$) stochastic cubic matrices satisfying…
We study a substitute for the matrix product ansatz for Asymmetric Simple Exclusion Process with open boundary in the ``singular case'' $\alpha\beta=q^N\gamma\delta$, when the standard form of the matrix product ansatz of Derrida, Evans,…
Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. The ability to implement these with high accuracy in…
We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald…
Motivated by queueing systems with heterogeneous parallel servers, we consider a class of structured multi-dimensional Markov processes whose state space can be partitioned into two parts: a finite set of boundary states and a structured…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as…
Consider the random process (Xt) solution of dXt/dt = A(It) Xt where (It) is a Markov process on {0,1} and A0 and A1 are real Hurwitz matrices on R2. Assuming that there exists lambda in (0, 1) such that (1 - \lambda)A0 + \lambdaA1 has a…
In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The…
A soliton cellular automaton associated with crystals of symmetric tensor representations of the quantum affine algebra U'_q(A^{(1)}_M) is introduced. It is a crystal theoretic formulation of the generalized box-ball system in which…
We present an algorithmic construction scheme for matrix-product-operator (MPO) representations of arbitrary $U(1)$-invariant operators whenever there is an expression of the local structure in terms of a finite-states machine (FSM). Given…
Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters q,t in [0,1). We prove several results about these…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…
Let $S$ be the multiplicative semigroup of $q\times q$ matrices with positive entries such that every row and every column contains a strictly positive element. Denote by $(X_n)_{n\geq1}$ a sequence of independent identically distributed…