Related papers: Weak Gibbs measures and large deviations

We consider translation-invariant interacting particle systems on the lattice with finite local state space admitting at least one Gibbs measure as a time-stationary measure. The dynamics can be irreversible but should satisfy some mild…

We study the charge dynamics of a quantum dot as measured by a nearby quantum point contact probing the dot via individual single-particle wave packets. We contrast the two limiting cases of weak and strong system--detector coupling…

Current quantum computer technology is sufficient to realize weak measurements and the corresponding concept of weak values. We demonstrate how the weak value anomaly can be tested, along with consistency and simultaneity of weak values,…

It will be established that the mean oscillation of a function on a metric-measure space $X\times Y$ will be small if its mean oscillation on $X$ is small and some simple information on its (partial $Y$) upper-gradient is given.…

We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbol{\lambda} \cdot \boldsymbol{\tilde{H}}$, $\boldsymbol{\lambda}= \{\lambda_1, \lambda_2,...\}$, $\boldsymbol{\tilde{H}}$ $=…

We obtain large deviation bounds for the measure of deviation sets associated to asymptotically additive and sub-additive potentials under some weak specification properties. In particular a large deviation principle is obtained in the case…

This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral…

We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…

We consider a hard core (HC) model with a countable set $\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $\lambda_{i}>0, i \in \mathbb{Z}\setminus\{0\}$. For all possible values of…

We investigate, in a fairly general setting, the limit of large volume equilibrium Gibbs measures for elasticity type Hamiltonians with clamped boundary conditions. The existence of a quasiconvex free energy, forming the large deviations…

Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…

The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an…

This paper is concerned with the study of fuzzy dynamical systems. Let (X;M; *) be a fuzzy metric space in the sense of George and Veeramani. A fuzzy discrete dynamical system is given by any fuzzy continuous self-map defined on X. We…

We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise…

It is perhaps not widely recognized that certain common notions of distance between probability measures have an alternative dual interpretation which compares corresponding functionals against suitable families of test functions. This dual…

We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…

We express continuous $\times p,\times q$-invariant measures on the unit circle via some simple forms. On one hand, a continuous $\times p,\times q$-invariant measure is the weak-$*$ limit of average of Dirac measures along an irrational…

One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic…

In this paper we will consider the concept of $\mathbb{P}$-weakly hyperbolic iterated function systems on compact metric spaces that generalizes the concept of weakly hyperbolic iterated function systems, as defined by Edalat in \cite{E}…

Weakly Interacting Massive Particles (WIMPs) are one of the leading candidates for Dark Matter. We developed a model-independent method for determining the WIMP mass by using data (i.e., measured recoil energies) of direct detection…