Related papers: Markov loops, determinants and Gaussian fields

We review the relations that have been found between multi-loop scattering amplitudes in gauge theory and gravity, and their implications for ultraviolet divergences in supergravity.

The purpose of this short paper is to give a summary of the derivation of a perturbative method to assess the impact of an arbitrary 3D magnetic field configuration, whose energy is everywhere small relative to the gravitational binding…

We discuss here the possibility to write the Liouville-Vlasov equation for the Wigner-function of a spinor field coupled to a gauge field with field strength tensor $F^{\mu\nu}$ in a curved space-time versus a local Lorentz manifold…

Motivated by change point problems in time series and the detection of textured objects in images, we consider the problem of detecting a piece of a Gaussian Markov random field hidden in white Gaussian noise. We derive minimax lower bounds…

In previous work the authors analysed the global properties of an approximate model of radiation damping for charged particles. This work is put into context and related to the original motivation of understanding approximations used in the…

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…

The relation between tempered distributions and measures is analysed and clarified. While this is straightforward for positive measures, it is surprisingly subtle for signed or complex measures.

Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.

A combination of observation, theory, modeling, and laboratory plasma experiments provides a multifaceted approach to develop a much greater understanding of how magnetic fields arise in galactic settings and how these magnetic fields…

This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…

see the old abstract and the comments here.

The usual prescription for constructing gauge-invariant Lagrangian is generalized to the case where a Lagrangian contains second derivatives of fields as well as first derivatives. Symmetric tensor fields in addition to the usual vector…

The purpose of this note is to clarify the logical relationship between joint measurability and contextuality for quantum observables in view of recent developments [1-4].

We present a theory for the estimation of a scalar or a vector magnetic field by its influence on an ensemble of trapped spin polarized atoms. The atoms interact off-resonantly with a continuous laser field, and the measurement of the…

We study Poissonian ensembles of Markov loops and the associated renormalized self-intersection local times.

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…

This paper is a review of the relationship between the metric formulation of (2+1)-dimensional gravity and the loop observables of Rovelli and Smolin. I emphasize the possibility of reconstructing the geometry, via the theory of geometric…

The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…

In the framework of Matrix theory we show that Wilson loops can serve as interpolating fields to define string scattering amplitudes as gauge theory observables.

We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the…