相关论文: Infinite Invariant Density Determines Statistics o…

For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. We are interested in the extension of the Donsker-Varadhan theory for a large size non-equilibrium…

This paper addresses the problem of identifying a linear time-varying (LTV) system characterized by a (possibly infinite) discrete set of delays and Doppler shifts. We prove that stable identifiability is possible if the upper uniform…

Under the assumption that sequences of graphs equipped with resistances, associated measures, walks and local times converge in a suitable Gromov-Hausdorff topology, we establish asymptotic bounds on the distribution of the…

The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…

The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…

A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only…

Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…

We characterize new universal features of the dynamics of chaotic quantum many-body systems, by considering a hypothetical task of "time estimation." Most macroscopic observables in a chaotic system equilibrate to nearly constant late-time…

A time-invariant, linear, distributed observer is described for estimating the state of an $m>0$ channel, $n$-dimensional continuous-time linear system of the form $ \dot{x} = Ax,\ y_i = C_i x,\ i \in \{1,2,\cdots, m\}$. The state $x$ is…

We investigate the properties of absolutely continuous invariant probability measures (ACIPs), especially those measures with bounded variation densities, for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps…

Using the supersymmetric method of random matrix theory within the Heidelberg approach framework we provide statistical description of stationary intensity sampled in locations inside an open wave-chaotic cavity, assuming that the…

This paper considers the problem of controlling a piecewise continuously differentiable system subject to time-varying uncertainties. The uncertainties are decomposed into a time-invariant, linearly-parameterized portion and a time-varying…

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

The irreducible decomposition of successive restriction and induction of irreducible representations of a symmetric group gives rise to a Markov chain on Young diagrams keeping the Plancherel measure invariant. Starting from this Res-Ind…

We address the question of representativeness of a single long unstable periodic orbit for properties of the chaotic attractor it is embedded in. Y. Saiki and M. Yamada [Phys. Rev. E 79, 015201(R) (2009)] have recently suggested the…

In this work we present analytical and numerical evidences that classical integrable models possessing infinitely many degrees of freedom unexpectedly exhibit some features that are typical of chaotic systems. By studying how the conserved…

Two dynamical indicators, the local dimension and the extremal index, used to quantify persistence in phase space have been developed and applied to different data across various disciplines. These are computed using the asymptotic limit of…