相关论文: Time functions and $K$-causality between measures

I want to show situations in which causal relation of two events is entangled and similar to time paradox, without employing time machines. Such situations will be obtained in measurement by two measurement devices moving mutually.…

We propose and study a new approach to the topologization of spaces of (possibly not all) future-directed causal curves in a stably causal spacetime. It relies on parametrizing the curves "in accordance" with a chosen time function. Thus…

We provide a framework and explicit construction for the regularized measurement of a large class of spacetime-localized observables in bosonic quantum field theory. The measurements fully satisfy relativistic causality and causal…

We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…

Recent works have proposed the use of the formalism of Positive Operator Valued Measures to describe time measurements in quantum mechanics. This work aims to expand on the work done by other authors, by generalizing the previously proposed…

In general relativity, time functions are crucial objects whose existence and properties are intimately tied to the causal structure of a spacetime and also to the initial value formulation of the Einstein equations. In this work we…

We discuss the usual account of causal structure that relies on the temporal precedence constraint between cause-effect pairs. In particular, we consider the subtle interplay between local and global characters of time and causality encoded…

We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives raise to a rich variety of novel asymmetric MK divergences, which subsume…

Most of the metrics used for detecting a causal relationship among multiple time series ignore the effects of practical measurement impairments, such as finite sample effects, undersampling and measurement noise. It has been shown that…

The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…

Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…

We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a…

We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…

This paper investigates the problem of extending measure theory to non-separable structures, from generalized descriptive set theory to a broader class of spaces beyond this framework. While various notions, such as the ideal of measure…

Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related…

We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects…

We study properties of causal couplings for probability measures on the space of continuous functions. We first provide a characterization of bicausal couplings between weak solutions of stochastic differential equations. We then provide a…

With any convex function F on a finite-dimensional linear space X such that F goes to infinity at infinity, we associate a Borel measure on the dual space X*. This measure is obtained by pushing forward the measure exp(-F(x))dx under the…

I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers Kronig relations. The specification of causality in terms of temporal differential eqations then shows us the way to write down dynamical…

Conventionally, covariances do not distinguish between spatial and temporal correlations. The same covariance matrix could equally describe temporal correlations between observations of the same system at two different times or correlations…