Related papers: The Almost Sure Invariance Principle for Beta-Mixi…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…
We show that if an infinite measure preserving system is well approximated on most of the phase space by a system satisfying the local limit theorem, then the original system enjoys mixing with respect to global observables, that is, the…
We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We first point out that a recent theory due to Pfister implies that for block-transformed measures free energies and relative…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…
The BBM equation is a Hamiltonian PDE which revealed to be a very interesting test-model to study the transformation property of Gaussian measures along the flow. In this paper we study the BBM equation with critical dispersion (which is a…
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting…
We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…
We prove the Almost Sure Invariance Principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing…
MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the…
The paper shows that, for large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the $W$ microstates of the famous Boltzmann-Planck entropy formula $S=k \log(W)$ is…
In this paper we study a class of \emph{self-consistent dynamical systems}, self-consistent in the sense that the discrete time dynamics is different in each step depending on current statistics. The general framework admits popular…
The Maximum Entropy Principle (MEP) is a method that can be used to infer the value of an unknown quantity in a set of probability functions. In this work we review two applications of MEP: one giving a precise inference of the Higgs boson…
Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less…
We study an information-theoretic measure of uncertainty for quantum systems. It is the Shannon information $I$ of the phase space probability distribution $\la z | \rho | z \ra $, where $|z \ra $ are coherent states, and $\rho$ is the…
Rare events attract more attention and interests in many scenarios of big data such as anomaly detection and security systems. To characterize the rare events importance from probabilistic perspective, the message importance measure (MIM)…
Let $T \colon M \to M$ be a nonuniformly expanding dynamical system, such as logistic or intermittent map. Let $v \colon M \to \mathbb{R}^d$ be an observable and $v_n = \sum_{k=0}^{n-1} v \circ T^k$ denote the Birkhoff sums. Given a…
This paper provides a complete proof of Simon-Lukic conjecture for orthogonal polynomials on the unit circle. For a probability measure $d\mu = w(\theta) \frac{d\theta}{2\pi} + d\mu_s$ with Verblunsky coefficients…