Related papers: Notes on Markov embedding

In this paper, we discuss the embedding problem for centrosymmetric matrices, which are higher order generalizations of the matrices occurring in Strand Symmetric Models. These models capture the substitution symmetries arising from the…

The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, involves the solution of a system of linear…

This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…

Quantum Markov models are employed ubiquitously in quantum physics and in quantum information theory due to their relative simplicity and analytical tractability. In particular, these models are known to give accurate approximations for a…

Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental…

Centraliser algebras of monomial representations of finite groups may be constructed and studied using methods similar to those employed in the study of permutation groups. Guided by results of D. G. Higman and others, we give an explicit…

We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the…

Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…

The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…

We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show…

Generators of Markov processes on a countable state space can be represented as finite or infinite matrices. One key property is that the off-diagonal entries corresponding to jump rates of the Markov process are non-negative. Here we…

A quantum Markov semigroup can be represented via classical diffusion processes solving a stochastic Schr\"odinger equation. In this paper we first prove that a quantum Markov semigroup is irreducible if and only if classical diffusion…

We introduce a class of so called Markovian marginals, which gives a natural framework for constructing solutions to the quantum marginal problem. We consider a set of marginals that possess a certain internal quantum Markov chain…

We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…

We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…