相关论文: Entropy method for the left tail

We establish a connection between barcode entropy and metric entropy. Namely, we show that the barcode entropy bounds the metric entropy from below for a measure from a specific class of invariant measures associated with a pair of…

A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…

We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…

We significantly improve the generalization bounds for VC classes by using two main ideas. First, we consider the hypergeometric tail inversion to obtain a very tight non-uniform distribution-independent risk upper bound for VC classes.…

Hoeffding has shown that tail bounds on the distribution for sampling from a finite population with replacement also apply to the corresponding cases of sampling without replacement. (A special case of this result is that binomial tail…

We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or…

In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary…

The tilings of lozenges in 2 dimensions and of rhomboedra in 3 dimensions are studied when they are constrained by fixed boundary conditions. We establish a link between those conditions and free or periodic boundary ones: the entropy is…

We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…

In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…

We demonstrate and discuss the process of gaining information and show an example in which some specific way of gaining information about an object results in the Tsallis form of entropy rather than in the Shannon one.

Two general upper bounds on the topological entropy of nonlinear time-varying systems are established: one using the matrix measure of the system Jacobian, the other using the largest real part of the eigenvalues of the Jacobian matrix with…

Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail…

Motivated by the approach of random linear codes, a new distance in the vector space over a finite field is defined as the logarithm of the "surface area" of a Hamming ball with radius being the corresponding Hamming distance. It is named…

We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.

Chernoff bounds are a powerful application of the Markov inequality to produce strong bounds on the tails of probability distributions. They are often used to bound the tail probabilities of sums of Poisson trials, or in regression to…

In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems…

In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…

We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a combination of time delay and spatial embedding.…

The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the…