Related papers: A Generalization of Relative Entropy to Count Vect…
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,…
We use the relative modular operator to define a generalized relative entropy for any convex operator function g on the positive real line satisfying g(1) = 0. We show that these convex operator functions can be partitioned into convex…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
We prove the bulk universality of the $\beta$-ensembles with non-convex regular analytic potentials for any $\beta>0$. This removes the convexity assumption appeared in our earlier work. The convexity condition enabled us to use the…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…
We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in…
We consider the problem of minimizing a generalized relative entropy, with respect to a reference diffusion law, over the set of path-measures with fully prescribed marginal distributions. When dealing with the actual relative entropy,…
We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…
In this paper, we establish the existence of the efficient solutions for polynomial vector optimization problems on a nonempty closed constraint set without any convexity and compactness assumptions. We first introduce the relative…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
We study the rigidity of the volume entropy for weighted word metrics on hyperbolic groups, building on a recent convexity result due to Cantrell-Tanaka. Using ideas from small cancellation theory, we give conditions under which a…
This paper focuses on the problem of finding a distribution for an associated entropic vector in the entropy space nearest to a given, possibly non-entropic, target vector for random variables with a constraint on alphabet size. We show the…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…
We consider relative entropy in Field Theory as a well defined (non-divergent) quantity of interest. We establish a monotonicity property with respect to the couplings in the theory. As a consequence, the relative entropy in a field theory…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
We provide a streamlined proof and improved estimates for the weak multivariate Gnedenko law of large numbers on concentration of random polytopes within the space of convex bodies (in a fixed or a high dimensional setting), as well as a…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…