Related papers: Variational principle and almost quasilocality for…
The article presents a systematic study of the problem of conditioning a Gaussian random variable $\xi$ on nonlinear observations of the form $F \circ \phi(\xi)$ where $\phi: \mathcal{X} \to \mathbb{R}^N$ is a bounded linear operator and…
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article…
Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical…
In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the…
The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary…
This paper aims at developing a quasi-Bayesian analysis of the nonparametric instrumental variables model, with a focus on the asymptotic properties of quasi-posterior distributions. In this paper, instead of assuming a distributional…
We show that in a generic scalar-tensor theory of gravity, the ``referenced'' quasilocal mass of a spatially bounded region in a classical solution is invariant under conformal transformations of the spacetime metric. We first extend the…
Power-law distributions are widely observed in complex systems, yet establishing their thermodynamic consistency remains a theoretical challenge. In this paper, we present a thermodynamic framework for power-law statistics based on the…
Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction…
We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann's and Gibbs' entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
An inverse problem of the determination of an initial condition in a hyperbolic equation from the lateral Cauchy data is considered. This problem has applications to the thermoacoustic tomography, as well as to linearized coefficient…
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…
We propose a non-Gaussianity measure of a multimode quantum state based on the negentropy of quadrature distributions. Our measure satisfies desirable properties as a non-Gaussianity measure, i.e., faithfulness, invariance under Gaussian…
We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All…
We pose the converse Madelung question: not whether Fisher information can reproduce quantum mechanics, but whether it is necessary. We work with minimal, physically motivated axioms on density and phase: locality, probability conservation,…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Repeated measurements can induce entanglement phase transitions in the dynamics of quantum systems. Interacting models, both chaotic and integrable, generically show a stable volume-law entangled phase at low measurement rates which…