相关论文: Marked Gibbs measures via cluster expansion

We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of $\operatorname{SL}(2,\mathbb{R})$ on smooth manifolds. Our main technical result, from which the rest of the…

Manifest gauge-invariance requires that observable states in the standard-model are described by composite operators, which involve additional Higgs contributions beyond perturbation theory. This field-theoretical effect has been confirmed…

We present numerical support for the hypothesis that macroscopic observables of dense granular media can be evaluated from averages over typical blocked configurations: we construct the corresponding measure for a class of…

We consider the canonical ensemble of a system of point particles on the sphere interacting via a logarithmic pair potential. In this setting, we study the associated Gibbs measure and partition function, and we derive explicit formulas…

We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…

We show how to estimate a broad class of multipartite entanglement measures from Bell basis measurement data. In addition to lowering the experimental requirements relative to previously known methods of estimating these measures, our…

Cover time, in the context of dynamical systems, quantifies the rate at which orbits cover the system. We prove that for countable full shifts with a Gibbs measure, equipped with a natural metric, the rate of covering of orbits of points…

Compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict…

We present a construction of a compact connected space which supports a normal probability measure.

The paradigm of measurement-based quantum computation opens new experimental avenues to realize a quantum computer and deepens our understanding of quantum physics. Measurement-based quantum computation starts from a highly entangled…

Excited-state electronic structure in strongly correlated systems remains challenging due to the exponential scaling of the many-body Hilbert space and the difficulty of constructing systematically controlled active spaces. Building on the…

Quantum metrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilizing entanglement and nonclassicality. However, the hurdle of actually implementing the necessary quantum probe states and…

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…

Cluster states serve as the central physical resource for the measurement-based quantum computation. We here present a simple experimental demonstration of the scalable cluster-state-construction scheme proposed by Browne and Rudolph. In…

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement…

Consider a compact metric space $(M, d_M)$ and $X = M^{\mathbb{N}}$. We prove a Ruelle's Perron Frobenius Theorem for a class of compact subshifts with Markovian structure introduced in [Bull. Braz. Math. Soc. 45 (2014), pp. 53-72] which…

Identifying a suitable set of descriptors for modeling physical systems often utilizes either deep physical insights or statistical methods such as compressed sensing. In statistical learning, a class of methods known as structured sparsity…

We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…

Understanding the formation and evolution of young star clusters requires quantitative statistical measures of their structure. We investigate the structures of observed and modelled star-forming clusters. By considering the different…

Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit…