Related papers: Quantization dimension for Gibbs-like measures on …
This paper discovers a new phenomenon about the Duffin-Schaeffer conjecture, which claims that $\lambda(\cap_{m=1}^{\infty}\cup_{n=m}^{\infty}{\mathcal E}_n)=1$ if and only if $\sum_n\lambda({\mathcal E}_n)=\infty$, where $\lambda$ denotes…
We establish conditions to characterize probability measures by their $L^{p}$-quantization error functions in both $\mathbb{R}^{d}$ and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic…
We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class $C_b^k$ with respect to appropriate reference measures. The case…
Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
If $\phi$ is a submeasure satisfying an appropriate lower estimate we give a quantitative result on the total mass of a measure $\mu$ satisfying $0\le\mu\le\phi.$ We give a dual result for supermeasures and then use these results to…
Fabrication and characterization of instrument for high-temperature simultaneous measurement of Seebeck coefficient (S) and thermal conductivity ($\kappa$) has been carried out with python automation. The steady-state based Fourier's law of…
Recently there has been interest in pairs of Banach spaces $(E_0,E)$ in an $o-O$ relation and with $E_0^{**}=E$. It is known that this can be done for Lipschitz spaces on suitable metric spaces. In this paper we consider the case of a…
We show that in doubling, geodesic metric measure spaces (including, for example, Euclidean space), sets of positive measure have a certain large-scale metric density property. As an application, we prove that a set of positive measure in…
We derive the focusing $\Phi^6_1$ measure on the torus $\mathbb{T}$ as the high-temperature/mean-field limit of many-body quantum Gibbs states with an attractive three-body interaction. The main difficulty in the focusing setting is to…
In this article, we further develop the thermodynamic formalism of affine iterated function systems with countably many transformations by showing the existence and extending earlier characterisations of the equilibrium states of finite…
It is shown that the temperature may be quantized in some spacetime due to the periodically topological structure of the Euclidean section. The quanta of the temperature is the Hawking-Unruh temperature.
Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the integrability of many probabilistic systems,…
Recent experiments show that double layer quantum Hall systems may have a ground state with canted antiferromagnetic order. In the experimentally accessible vicinity of a quantum critical point, the order vanishes at a temperature T_{KT} =…
We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse…
Let \(\mu\) be a finite Borel measure on \((-\pi,\pi)\). Consider the one-dimensional Poisson equation \(-u''=\mu\), where equality holds in the sense of distributions, with Dirichlet boundary conditions \(u(\pm\pi)=0\). In this paper, we…
Asynchronous Gibbs sampling has been recently shown to be fast-mixing and an accurate method for estimating probabilities of events on a small number of variables of a graphical model satisfying Dobrushin's condition~\cite{DeSaOR16}. We…
Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and…