Related papers: On singular limits of relative entropies

In these proceedings we give a pedagogical and non-technical introduction to the Quantum Field Theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation,…

We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime…

We develop the relative Morse index theory for linear self-adjoint operator equation without compactness assumption and give the relationship between the index defined in [44] and [45]. Then we generalize the method of saddle point…

This paper uses a net-theoretic approach to convergence spaces, aimed to simplify the description of continuous convergence in order to apply it in problems concerning Homotopy Theory. We present methods for handling homotopies of limit…

The purpose of this work is to bound sofic topological entropy of Toeplitz systems over residually finite groups and to prove the Krieger Theorem about attaining arbitrary entropy by the Toeplitz systems. To achieve these results, we…

This article presents in a self-contained way A. Uhlmann's celebrated Theorem of monotonicity of the relative entropy under completely positive and trace preserving maps. The Theorem is presented in its more general form and meaningful…

We consider single interval R\'enyi and entanglement entropies for a two dimensional conformal field theory on a circle at nonzero temperature. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass…

We extend Lyons's tree entropy theorem to general determinantal measures. As a byproduct we show that the sofic entropy of an invariant determinantal measure does not depend on the chosen sofic approximation.

In this note, we explain how to prove several basic results about finite index extensions of irreducible local M\"obius covariant nets in the setting of Connes fusion.

Some recent existence, multiplicity, and uniqueness results for singular p-Laplacian systems either in bounded domains or in the whole space are presented, with a special attention to the case of convective reactions. A extensive…

We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…

We show that in any relativistic system, entanglement entropy obeys a speed limit set by the entanglement in thermal equilibrium. The bound is derived from inequalities on relative entropy with respect to a thermal reference state. Thus the…

In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (2018) and references therein] to treat more general kernels…

We discuss different generalizations of the classical notion of the index of a singular point of a vector field to the case of vector fields or 1-forms on singular varieties, describe relations between them and formulae for their…

The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and…

We introduce the concept of \textit{defect relative entropy} as a measure of distinguishability within the space of defects. We compute the defect relative entropy for conformal/topological defects, deriving a universal formula in conformal…

We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…

This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…

A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…

The specific relative entropy, introduced by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of…