Related papers: Rigidity of Furstenberg entropy under ucp maps

We prove that generically in $\text{Diff}^{1}_{m}(M)$, if an expanding $f$-invariant foliation $W$ of dimension $u$ is minimal and there is a periodic point of unstable index $u$, the foliation is stably minimal. By this we mean there is a…

In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…

For the general class of quasifree fermionic right mover/left mover systems over the infinitely extended two-sided discrete line introduced in [8] within the algebraic framework of quantum statistical mechanics, we study the von Neumann…

The measure contraction property, $\mathsf{MCP}$ for short, is a weak Ricci curvature lower bound conditions for metric measure spaces. The goal of this paper is to understand which structural properties such assumption (or even weaker…

Understanding and quantifying entanglement entropy is crucial to characterize the quantum behaviors that drive phenomena in a variety of systems. Rare-earth spin complexes, with their unique magnetic properties, provide fertile ground for…

In this paper we study R-reversible area-preserving maps f on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that Ro f=f^{-1}o R where R is an isometric involution on M. We obtain a C1-residual subset where any…

We define various notions of locality for *-automorphisms of the algebra of observables for an infinitely extended quantum spin system and study their relationship. In particular, we show that the ubiquitous characterization which arises…

We used the von Neumann entropy to study the single and many-particle on-site localizations of stationary states for an anisotropic Heisenberg spin-1/2 chain. With a constructed bounded sequence of on-site energies for single and…

There is a qualitative difference between one-dimensional and multi-dimensional solutions to the Euler equations: new features that arise are vorticity and a nontrivial incompressible (low Mach number) limit. They present challenges to…

This paper displays the Healy-McInnes UMAP construction $V(X,N)$ as an iterated pushout of Vietoris-Rips objects associated to extended pseudo metric spaces (ep-metric spaces) defined by choices of neighbourhoods of the elements of a finite…

We study a notion of tight inclusions of C*- and W*-dynamical systems which is meant to capture a tension between topological and measurable rigidity of boundary actions. An important case of such inclusions are $C(X)\subset L^\infty(X,…

Schoenberg transformations, mapping Euclidean configurations into Euclidean configurations, define in turn a transformed inertia, whose minimization produces robust location estimates. The procedure only depends upon Euclidean distances…

We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational…

We apply Hilbert module methods to show that normal completely positive maps admit weak tensor dilations. Appealing to a duality between weak tensor dilations and extensions of CP-maps, we get an existence proof for certain extensions. We…

Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…

We establish rigidity theorems for graph product von Neumann algebras $M_\Gamma=*_{v,\Gamma}M_v$ associated to finite simple graphs $\Gamma$ and families of tracial von Neumann algebras $(M_v)_{v\in\Gamma}$. We consider the following three…

We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of…

In this article, we prove a general viability theorem for continuity inclusions in Wasserstein spaces, and provide an application thereof to the existence of exponentially stable trajectories obtained via the second method of Lyapunov.

Exploiting a construction of rigidity sequences for weakly mixing dynamical systems by Fayad and Thouvenot, we show that for every integers $p_{1},\dots,p_{r}$ there exists a continuous probability measure $\mu $ on the unit circle…

Let $G$ be a graph and suppose we are given, for each $v \in V(G)$, a strict ordering of the neighbors of $v$. A set of matchings ${\cal M}$ of $G$ is called internally stable if there are no matchings $M,M' \in {\cal M}$ such that an edge…