Related papers: Confined Poisson extensions

We give out the time evolution solution of simultaneous amplitude and phase damping for any continuous variable state. For the simultaneous amplitude and phase damping of a wide class of two- mode entangled Gaussian states, two analytical…

Let $G$ be a countable residually finite group (for instance $\mathbb{F}_2$) and let $\overleftarrow{G}$ be a totally disconnected metric compactification of $G$ equipped with the action of $G$ by left multiplication. For every $r\geq 1$ we…

We obtain some results of existence and continuity of physical measures through equilibrium states and apply these to non-uniformly expanding transformations on compact manifolds with non-flat critical sets, obtaining sufficient conditions…

We discuss the relationship between discrete-time processes (chains) and one-dimensional Gibbs measures. We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic…

Given a countable group $G$ and two subshifts $X$ and $Y$ over $G$, a continuous, shift-commuting map $\phi : X \to Y$ is called a homomorphism. Our main result states that if every finitely generated subgroup of $G$ has polynomial growth,…

Let $(X,d,f)$ be a topological dynamical system, where $(X,d)$ is a compact metric space and $f:X\to X$ is a continuous map. We define $n$-ordered empirical measure of $x\in X$ by \begin{align*}…

We study several notions of topological pressure and capacities for multi-potentials $\Phi \in \mathcal C(X;\mathbb R)^m$, with respect to finitely generated continuous semigroups $G$ on a compact metric space $X$. We introduce the…

We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighted inequalities, which are new. As an application, we prove…

In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…

We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of…

I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…

The anticommuting properties of fermionic operators, together with the presence of parity conservation, affect the concept of entanglement in a composite fermionic system. Hence different points of view can give rise to different reasonable…

Let $(X,\mathcal{B},\mu,T)$ be a measure preserving system. We say that a function $f\in L^2(X,\mu)$ is $\mu$-mean equicontinuous if for any $\epsilon>0$ there is $k\in \mathbb{N}$ and measurable sets ${A_1,A_2,\cdots,A_k}$ with…

Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…

Motivated, in part, by the desire to develop an information-theoretic foundation for compound Poisson approximation limit theorems (analogous to the corresponding developments for the central limit theorem and for simple Poisson…

We introduce the notion of localized topological pressure for continuous maps on compact metric spaces. The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose…

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…

Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…

Definable subcategories may be extended along a ring homomorphism directly, by using their defining conditions in the new module category, or by tensoring up with the new ring. We investigate what is preserved and reflected by these…

Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less…