相关论文: Why the Kemeny Time is a Constant
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…
When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This is done by considering as basic uncertainty models the so-called credal sets that…
Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an i.i.d. process. A key step is to show that any…
A review of new aspects concerning time-symmetry in Quantum Mechanics.
In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. The quantum Markov chain, like the classical Markov chain, is a fundamental tool for the investigation of the basic properties such…
We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The…
We improve constants in the Rademacher-Menchov inequality.
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Time plays a fundamental role in our ability to make sense of the physical laws in the world around us. The nature of time has puzzled people -- from the ancient Greeks to the present day -- resulting in a long running debate between…
Substitution Markov chains have been introduced [7] as a new model to describe molecular evolution. In this note, we study the associated Martin boundaries from a probabilistic and topological viewpoint. An example is given that, although…
In the present paper we study a unified approach for Quantum Markov Chains. A new quantum Markov property that generalizes the old one, is discussed. We introduce Markov states and chains on general local algebras, possessing a generic…
We describe a link between the cosmological constant problem and the problem of time in quantum gravity. This arises by examining the relationship between the cosmological constant and vacuum energy in light of non-perturbative formulations…
This article continues our study of Markovian consistency and Markov copulae. In particular, we characterize the weak Markovian consistency for finite Markov chains. We discuss some aspects of dependence between the components of a…
Understanding different aspects of time is at the core of many areas in theoretical physics. Minimal models of continuous stochastic and quantum clocks have been proposed to explore fundamental limitations on the performance of timekeeping…
It is well known that any higher order Markov chain can be associated with a first order Markov chain. In this primarily expository article, we present the first fairly comprehensive analysis of the relationship between higher order and…
In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
For a stochastically monotone Markov chain taking values in a Polish space, we present a number of conditions for existence and for uniqueness of its stationary regime, as well as for closeness of its transient trajectories. In particular,…
We examine the time variation of a previously-uninvestigated fundamental dimensionless constant. Constraints are placed on this time variation using historical measurements. A model is presented for the time variation, and it is shown to…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…