For the 2D matrix Langevin dynamics that correspond to the continuous-time limit of the
products of some 2× 2 random matrices, the finite-time Lyapunov exponent can be written as …

Volatility component models have received considerable attention recently, not only
because of their ability to capture complex dynamics via a parsimonious parameter …

Generic dynamical systems have'typical'Lyapunov exponents, measuring the sensitivity to
small perturbations of almost all trajectories. A generic system also has trajectories with …

The exact value of the Lyapunov exponents for the random matrix product PN= ANAN− 1⋯ A
1 with each A_i=\varSigma^1/2G_i^c, where Σ is a fixed d× d positive definite matrix and …

This thesis reviews recent progress on products of random matrices from the perspective of
exactly solved Gaussian random matrix models. We derive exact formulae for the correlation …

By computing the Lyapunov exponent, which is the inverse of the instability time scale
associated with this geodesic motion we show that for a general Kehagias-Sfetsos (KS) …

The dispersion of a passive scalar in a fluid through the combined action of advection and
molecular diffusion is often described as a diffusive process, with an effective diffusivity that …

The exploration of matrix products is closely tied to averaging dynamics, which arises from
decentralized information diffusion mechanisms in complex networked systems. Markov …

This monograph presents some new concentration inequalities for Feynman-Kac particle
processes. We analyze different types of stochastic particle models, including particle profile …

We develop a method to calculate left-right eigenvector correlations of the product of m
independent N× N complex Ginibre matrices. For illustration, we present explicit analytical …