Related papers: Cover time for countable Markov shifts

We consider killed Markov decision processes for countable models on a finite time-interval. Existence of a uniform $\varepsilon$-optimal policy is proven. We show the correctness of the fundamental equation. The optimal control problem is…

In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…

I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special…

The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…

We define a physically-motivated measure for galactic bar length, called the dynamical length. The dynamical length of the bar corresponds to the radial extent of the orbits that are the backbone supporting the bar feature. We propose a…

Let $\{B(\xi_n,r_n)\}_{n\ge1}$ be a sequence of random balls whose centers $\{\xi_n\}_{n\ge1}$ is a stationary process, and $\{r_n\}_{n\ge1}$ is a sequence of positive numbers decreasing to 0. Our object is the random covering set…

In this paper we introduce three notions of measure theoretical entropy of a measurable cover U in a measure theoretical dynamical system. Two of them were already introduced in [R] and the new one is defined only in the ergodic case. We…

Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…

The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…

Several authors have shown that Kusuoka's measure $\kappa$ on fractals is a scalar Gibbs measure; in particular, it maximises a pressure. There is also a different approach, in which one defines a matrix-valued Gibbs measure $\mu$ which…

Suppose A is a finite set equipped with a probability measure P and let M be a ``mass'' function on A. We give a probabilistic characterization of the most efficient way in which A^n can be almost-covered using spheres of a fixed radius. An…

Taking into account the mass transfer effect, we derive the equations of motion of a compact binary system at the second-half post-Newtonian order. Applying such equations of motion to quasi-circular orbits, we obtain the time derivative of…

We consider an absorbing Markov decision process with Borel state and action spaces. We study conditions under which the MDP is uniformly absorbing and the set of occupation measures of the MDP is compact in the usual weak topology. These…

If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of…

Let 0<\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \alpha of the state space.…

We give a survey of various recent developments in orbit equivalence and measured group theory. This subject aims at studying infinite countable groups through their measure preserving actions.

Estimating the parameters that dictate the dynamics of a quantum system is an important task for quantum information processing and quantum metrology, as well as fundamental physics. In this paper we develop a method for parameter…

To make progress in understanding the issue of memory loss and history dependence in evolving complex systems, we consider the mixing rate that specifies how fast the future states become independent of the initial condition. We propose a…

Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter. Motivated by the physics of the Kitaev quantum spin liquid [1], we study quantum circuit dynamics in…

One of the most important topics in the study of the dynamics of open quantum system is information exchange between system and environment. Based on the features of a back-flow information from an environment to a system, an approach is…