相关论文: Random products of matrices: a dynamical point of …

We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent iid random matrices, as $M$ is fixed, and the sizes of the matrices tend to infinity. This…

A sofic measure is the image of a Markov probability measure by a continuous morphism, and can be represented by means of products of matrices $A_n$ that belong to a finite set of nonnegative matrices. To prove that the multifractal…

We consider random products of $SL(2, \mathbb{R})$ matrices that depend on a parameter in a non-uniformly hyperbolic regime. We show that if the dependence on the parameter is monotone then almost surely the random product has upper…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…

We study stochastic particle systems with stationary product measures that exhibit a condensation transition due to particle interactions or spatial inhomogeneities. We review previous work on the stationary behaviour and put it in the…

We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing…

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…

This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…

We find conditions which guarantee moment (in)determinacy of powers and products of nonnegative random variables. We establish new and general results which are based either on the rate of growth of the moments of a random variable or on…

We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…

We extend our previous study of Markov chains on finite commutative rings (arXiv:1605.05089) to arbitrary finite rings with identity. At each step, we either add or multiply by a randomly chosen element of the ring, where the addition…

We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential…

Let $\xi_1,\xi_2,...$ be independent identically distributed random variables and $F:\bbR^\ell\to SL_d(\bbR)$ be a Borel measurable matrix-valued function. Set $X_n=F(\xi_{q_1(n)},\xi_{q_2(n)},...,\xi_{q_\ell(n)})$ where $0\leq…

We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…

We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…

Suppose $\{ X_k \}_{k \in \mathbb{Z}}$ is a sequence of bounded independent random matrices with common dimension $d\times d$ and common expectation $\mathbb{E}[ X_k ]= X$. Under these general assumptions, the normalized random matrix…

Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…

We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound…