Related papers: Timelike boundary and corner terms in the causal s…

We undertake a systematic investigation of compact aspherical manifolds with boundary; motivated by the plethora of examples in the bounded case and by the beauty of the theory in the closed case. Our main theorems give a homological…

We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We…

The random motion of a Brownian particle confined in some finite domain is considered. Quite generally, the relevant statistical properties involve infinite series, whose coefficients are related to the eigenvalues of the diffusion…

General Relativity is contaminated with non-trivial geometries which generate closed timelike curves. These apparently violate causality, producing time-travel paradoxes. We shall briefly discuss these geometries and analyze some of their…

We apply a recent proposal for a distinguished ground state of a quantum field in a globally hyperbolic spacetime to the free massless scalar field in a causal diamond in two-dimensional Minkowski space. We investigate the two limits in…

This paper establishes connections between the boundary behaviour of functions representable as absolutely convergent Dirichlet series in a half-plane and the convergence properties of partial sums of the Dirichlet series on the boundary.…

In this paper, we consider a concentration of measure problem on Riemannian manifolds with boundary. We study concentration phenomena of non-negative $1$-Lipschitz functions with Dirichlet boundary condition around zero, which is called…

It is shown that causal automorphisms on two-dimensional Minkowski spacetime can be characterized by the invariance of the wave equations.

A simple characterization of the causal automorphisms of 1+1 Minkowski spacetime is given.

The new formulation of the causal completion of spacetimes suggested in [1], and modified later in [2], is tested by computing the causal boundary for product spacetimes of a Lorentz interval and a Riemannian manifold. This is…

Causal discovery is the subfield of causal inference concerned with estimating the structure of cause-and-effect relationships in a system of interrelated variables, as opposed to quantifying the strength or describing the form of causal…

While intersections of convex sets are convex, their unions have rather complicated behavior. Some natural contexts where they appear include duality arguments involving boundaries of convex sets and valuations, which have an Euler…

Using the explicit representations of the Brownian motions on the hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity are easily obtained. We also…

In the series of models with interacting particles in stochastic geometry, a new contribution presents the facet process which is defined in arbitrary Euclidean dimension. In 2D, 3D specially it is a process of interacting segments, flat…

A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the…

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 review a formulation of the entanglement entropy of a quantum scalar field in terms of its spacetime two-point correlation functions. We discuss applications of this formulation to studying entanglement entropy in various settings in…

A new approach for treating boundary Poisson structures based on causality and locality analysis is proposed for a single scalar field with boundary interaction. For the case of linear boundary condition, it is shown that the usual…

This paper presents an brief review of some recent work on the causal set approach to quantum gravity. Causal sets are a discretisation of spacetime that allow the symmetries of GR to be preserved in the continuum approximation. One…

The causal structure of space-time offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non time-like related with it. We show that for a general space-time the…