Products of Random Matrices

  title={Products of Random Matrices},
  author={Harry Furstenberg and Harry Kesten},
  journal={Annals of Mathematical Statistics},
Convergence in $$L^p$$ for a Supercritical Multi-type Branching Process in a Random Environment
Abstract Consider a $$d$$ -type supercritical branching process $$Z_n^i=(Z_n^i(1),\ldots,Z_n^i(d))$$ , $$n\geq 0$$ , in an independent and identically distributed random environment $$\xi
Non-asymptotic Results for Singular Values of Gaussian Matrix Products
This article concerns the non-asymptotic analysis of the singular values (and Lyapunov exponents) of Gaussian matrix products in the regime where $N,$ the number of term in the product, is large and
Performance analysis of asynchronous parallel Jacobi
This paper presents a formalism for analyzing the performance of asynchronous parallel Jacobi’s method in terms of its DAG, and uses this app.roach to prove error bounds and bounds on the rate of convergence.
Large excursions and conditioned laws for recursive sequences generated by random matrices
This work characterize the distribution of the first passage time of the matrix recursive sequence V_n = M_n V_{n-1} + Q_n, showing that this distribution converges to the stationary law of the exponentially-shifted Markov random walk and describes the large exceedance paths via two conditioned limit laws.
We show that for any n ≥ 2, two elements selected uniformly at random from a symmetrized Euclidean ball of radius X in SLn(Z) will generate a thin free group with probability tending to 1 as X → ∞.
Generic thinness in finitely generated subgroups of $\textrm{SL}_n(\mathbb Z)$
We show that for any $n\geq 2$, two elements selected uniformly at random from a \emph{symmetrized} Euclidean ball of radius $X$ in $\textrm{SL}_n(\mathbb Z)$ will generate a thin free group with
Recurrence and Transience of Random Walks¶in Random Environments on a Strip
Abstract: We explain the necessary and sufficient conditions for recurrent and transient behavior of a random walk in a stationary ergodic random environment on a strip in terms of properties of a
Sample ACF of Multivariate Stochastic Recurrence Equations With Application to GARCH
We study the weak limit behaviour of the sample autocorrelation function (ACF) of non-linear stationary sequences with regularly varying nite-dimensional distributions. In particular, we consider the
Convergence in distribution of products of random matrices
SummaryWe consider a sequence A2, A2, ... of i.i.d. nonnegative matrices of size d × d, and investigate convergence in distribution of the product Mn: =A1 ... An. When d≧2 it is possible for Mn to
Berry–Esseen bound and precise moderate deviations for products of random matrices
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed (i.i.d.) $d\times d$creal random matrices. Set $G_n = g_n g_{n-1} \ldots g_1$ and $X_n^x = G_n x/|G_n x|$, $n\geq 1$,


Stochastic processes