Related papers: Products of random matrices and queueing system pe…
We give lower and upper bounds on both the Lyapunov exponent and generalised Lyapunov exponents for the random product of positive and negative shear matrices. These types of random products arise in applications such as fluid stirring…
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for…
For arbitrary F-algebra, in which the operation of addition is defined, I explore biring of matrices of mappings. The sum of matrices is determined by the sum in F-algebra, and the product of matrices is determined by the product of…
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…
The paper deals with the convergence properties of the products of random (row-)stochastic matrices. The limiting behavior of such products is studied from a dynamical system point of view. In particular, by appropriately defining a dynamic…
In this paper, we disclose the statistical behavior of the max-product algorithm configured to solve a maximum a posteriori (MAP) estimation problem in a network of distributed agents. Specifically, we first build a distributed hypothesis…
An overview of the recursive equations based models and their applications in simulation based analysis and optimization of queueing systems is given. These models provide a variety of systems with a convenient and unified representation in…
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics, and the ones obtained by combining them, are often called performability measures. We show that this computational…
The production network under examination consists of a number of workstations. Each workstation is a parallel configuration of machines performing the same kind of tasks on a given part. Parts move from one workstation to another and at…
For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel…
Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed (V. Baldoni et al., 2011). In this note, we highlight that this problem is equivalent to obtaining the…
We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…
We define a class of "algebraic" random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner…
A random matrix with rows distributed as a function of their length is said to be isotropic. When these distributions are Gaussian, beta type I, or beta type II, previous work has, from the viewpoint of integral geometry, obtained the…
I present a general framework allowing to carry out explicit calculation of the moment generating function of random matrix products $\Pi_n=M_nM_{n-1}\cdots M_1$, where $M_i$'s are i.i.d.. Following Tutubalin [Theor. Probab. Appl. {\bf 10},…
In this short note, we study the behaviour of a product of matrices with a simultaneous renormalization. Namely, for any sequence $(A\_n)\_{n\in \mathbb{N}}$ of $d\times d$ complex matrices whose mean $A$ exists and whose norms' means are…
We present a method for randomizing formulas for bilinear computation of matrix products. We consider the implications of such randomization when there are two sources of error: One due to the formula itself only being approximately…
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…
In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asymptotic limits. The matrices in the product are taken from…