Related papers: Entropic Inequalities and Marginal Problems

We consider a new functional inequality controlling the rate of relative entropy decay for random walks, the interchange process and more general block-type dynamics for permutations. The inequality lies between the classical logarithmic…

The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this…

Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…

Source-sink systems are metapopulations of patches that can be of variable habitat quality. They can be seen as graphs, where vertices represent the patches, and the weighted oriented edges give the probability of dispersal from one patch…

We investigate whether the presence or absence of correlations between subsystems of an N-partite quantum system is solely constrained by the non-negativity and monotonicity of mutual information. We argue that this relatively simple…

Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…

We explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by J. Kujala et. al. [Phys. Rev. Lett. 115, 150401 (2015)] using graph-theoretical terms. This extended definition avoids the…

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 consider families of finite quantum graphs of increasing size and we are interested in how eigenfunctions are distributed over the graph. As a measure for the distribution of an eigenfunction on a graph we introduce the entropy, it has…

The contextuality problem connected with existence of joint probability distribution creating all the given marginals is studied. It is shown for several examples considered previously in literature that there exist some new solutions for…

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…

The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…

A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…

Calculating the Shannon entropy for symbolic sequences has been widely considered in many fields. For descriptive statistical problems such as estimating the N-gram entropy of English language text, a common approach is to use as much data…

One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…

We are concerned with the general problem of proving the existence of joint distributions of two discrete random variables $M$ and $N$ subject to infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In particular, the…

Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…

Quantifying the complexity of large graphs requires measures that extend beyond predefined structural features and scale efficiently with graph size. This work adopts a generative perspective, modeling large networks as exchangeable graphs…

Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…