相关论文: An Elementary Approach to Free Entropy Theory for …
We study the properties of pseudo entropy, a new generalization of entanglement entropy, in free Maxwell field theory in $d = 4$ dimension. We prepare excited states by the different components of the field strengths located at different…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
We study the asymptotics of complete Kaehler-Einstein metrics on strictly pseudoconvex domains in C^n and derive a convergence theorem for solutions to the corresponding Monge-Ampere equation. If only a portion of the boundary is analytic,…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate…
In this paper, we investigate the almost surely pointwise convergence problem of free KdV equation, free wave equation, free elliptic and non-elliptic Schr\"odinger equation respectively. We firstly establish some estimates related to the…
We consider models of gradient type, which are the densities of a collection of real-valued random variables $\phi :=\{\phi_x: x \in \Lambda\}$ given by $Z^{-1}\exp({-\sum\nolimits_{j \sim k}V(\phi_j-\phi_k)})$. We focus our study on the…
We introduce a generalised micro-macro Markov chain Monte Carlo (mM-MCMC) method with pseudo-marginal approximation to the free energy, that is able to accelerate sampling of the microscopic Gibbs distributions when there is a time-scale…
We present an analytical formula for the asymptotic relative entropy of entanglement for Werner states of arbitrary dimension. We then demonstrate its validity using methods from convex optimization. To our knowledge, this is the first case…
We propose a generalization of Grunberg's method of effective charges in which, starting with the effective charge for some dimensionless QCD observable dependent on the single energy scale $Q, R(Q)$, we introduce an infinite set of…
Some aspects of asymptotic freedom are discussed in the context of a simple two-particle non-relativisitic confining potential model. In this model asymptotic freedom follows from the similarity of the free-particle and bound state radial…
Convexity properties of the entropy along displacement interpolations are crucial in the Lott-Sturm-Villani theory of lower bounded curvature of geodesic measure spaces. As discrete spaces fail to be geodesic, an alternate analogous theory…
We study the flexibility of the pressure function of a continuous potential (observable) with respect to a parameter regarded as the inverse temperature. The points of non-differentiability of this function are of particular interest in…
The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…
We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…
We consider a random Hamiltonian $H:\Sigma\to\mathbb R$ defined on a compact space $\Sigma$ that admits a transitive action by a compact group $\mathcal G$. When the law of $H$ is $\mathcal G$-invariant, we show its expected free energy…
The problem of computing posterior functionals in general high-dimensional statistical models with possibly non-log-concave likelihood functions is considered. Based on the proof strategy of Nickl and Wang (2022), but using only local…
A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution…
We propose a novel approach to concentration for non-independent random variables. The main idea is to ``pretend'' that the random variables are independent and pay a multiplicative price measuring how far they are from actually being…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…