Related papers: Shrinking random $\beta$-transformation

We consider the convergence of the eigenvalues to the support of the equilibrium measure in the $\beta$ ensemble models under a critical condition. We show a phase transition phenomenon, namely that, with probability one, all eigenvalues…

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x_1^n using the entropy of the k-block empirical probability and letting k grow with $n$ roughly like log n. We further assume that the…

We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…

Countable Markov shifts, denoted by $\Sigma_A$ for a 0-1 infinite matrix $A$, are central objects in symbolic dynamics and ergodic theory. R. Exel and M. Laca introduced the corresponding operator algebras, a generalization of the…

We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…

The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…

We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a measurement-induced transition occurs between two…

We compare a piecewise linear map with constant slope beta>1 and a piecewise linear map with constant slope -beta. These maps are called the positive and negative beta-transformations. We show that for a certain set of beta's, the…

We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…

Invariance entropy is a measure for the smallest data rate in a noiseless digital channel above which a controller that only receives state information through this channel is able to render a given subset of the state space invariant. In…

Let $f$ be an holomorphic endomorphism of $\mathbb{C}\mathbb{P}^k$. We construct by using coding techniques a class of ergodic measures as limits of non-uniform probability measures on preimages of points. We show that they have large…

We consider constraints on the measure of the support for integrable functions on arbitrary measure spaces. It is shown that this non-convex and discontinuous constraint can be equivalently reformulated by the difference of two convex and…

A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…

We elaborate on a Hilbert-Schmidt distance measure assessing the intrinsic metrological accuracy in the detection of signals imprinted on quantum probe states by signal-dependent transformations. For small signals this leads to a…

Structural entropy is a metric that measures the amount of information embedded in graph structure data under a strategy of hierarchical abstracting. To measure the structural entropy of a dynamic graph, we need to decode the optimal…

In this paper we consider a semiparametric regression model involving a $d$-dimensional quantitative explanatory variable $X$ and including a dimension reduction of $X$ via an index $\beta'X$. In this model, the main goal is to estimate the…

The generalized entropic measure, which is optimized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity, is considered and its…

The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…

Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…

We present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a…