相关论文: Markov loops, determinants and Gaussian fields

The article investigates the following question: given a projective variety X acted on by a connected and reductive group G, which is the relationship between the Gromov-Witten invariants of X and those of X//G? In this study we shall also…

Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closeness between…

We focus on the interaction of a plane gravitational wave with electromagnetic fields and we describe this interaction in the proper detector frame where, thanks to the introduction of Fermi coordinates, it is possible to refer to directly…

The study of Gaussian states has arisen to a privileged position in continuous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In…

These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.

An interplay between electromagnetic and gravitational interactions is studied with particular emphasis on the particles mass dependence of amplitudes. The cancellations between diagrams due to the gauge invarinace are explicitly…

The goal of these lecture notes is to introduce the developing research area of gravitational-wave phenomenology. In more concrete terms, they are meant to provide an overview of gravitational-wave sources and an introduction to the…

We derive loop equations for the one-link correlators of gauge and scalar fields in the Kazakov-Migdal model. These equations determine the solution of the model in the large N limit and are similar to analogous equations for the Hermitean…

A configuration of a test magnetic field in Hayward spacetime is obtained by solving Maxwell's equation with the Hayward metric as the background. The magnetic field lines show a dipole loop-like configuration in the regular Hayward…

We calculate the magnetic-field dependent nonlinear conductance and noise in a macroscopic inhomogeneous system. If the system does not possess a specific symmetry, the magnetic field induces a nonzero third cumulant of the current even at…

The representation problem of finite-dimensional Markov matrices in Markov semigroups is revisited, with emphasis on concrete criteria for matrix subclasses of theoretical or practical relevance, such as equal-input, circulant, symmetric or…

The purpose of this survey is to present the recent advances about the Pollicott-Ruelle resonances.

Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian…

The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).

In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…

The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional…

Determining and measuring cause-effect relationships is fundamental to most scientific studies of natural phenomena. The notion of causation is distinctly different from correlation which only looks at association of trends or patterns in…

This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.

We report on the behaviour of two-level quantum systems, or qubits, in the background of rotating and non-rotating metrics and provide a method to derive the related spin currents and motions. The calculations are performed in the external…

Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…