相关论文: Markov loops, determinants and Gaussian fields

The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices…

In order to compute the log-likelihood for high dimensional spatial Gaussian models, it is necessary to compute the determinant of the large, sparse, symmetric positive definite precision matrix, Q. Traditional methods for evaluating the…

We review some attempts of reformulating both gauge theory and general relativity in terms of holonomy-dependent loop variables. The emphasis lies on exhibiting the underlying mathematical structures, which often are not given due attention…

Measurement of gravitomagnetic field is of fundamental importance as a test of general relativity. Here we present a new theoretical project for performing such a measurement based on detection of the electric field arising from the…

Gauge fields are described on an Riemann-Cartan space-time by means of tensor-valued differential forms and exterior calculus. It is shown that minimal coupling procedure leads to a gauge invariant theory where gauge fields interact with…

These Lecture Notes are a brief introduction to the Malliavin calculus. In particular, different notions of Malliavin derivative found in the literature are considered and compared.

The Law of the Iterated Logarithm for some Markov operators, which converge exponentially to the invariant measure, is established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell…

A certain determinant is evaluated by guessing and computing the LU-decomposition.

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained which includes derivatives of the curvature. We analyze the form of the second field…

The role of the measurement process in resolving the gauge ambiguity of the effective gravitational potential is reexamined. The motion of a classical point-like particle in the field of an arbitrary linear source, and in the field of…

These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…

We point out an incompleteness of formulations of gravitational and gauge theories that use traces of holonomies around closed curves as their basic variables. It is shown that in general such loop variables have to satisfy certain…

In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…

It is explained how techniques from microlocal analysis can be used to settle some long-standing questions that arise in the study of the interaction of quantum matter fields with a classical gravitational background field.

We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…

A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.

Gauge-fixed correlation functions are a valuable tool in intermediate steps when determining gauge-invariant physics. However, when obtaining them in different calculations, it is necessary to use exactly the same definition of the gauge to…

Model interactions between classical and quantum systems are briefly reviewed. These include: general measurement - like couplings, Stern-Gerlach experiment, model of a counter, quantum Zeno effect, piecewise deterministic Markov processes…

We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…

Torsion represents the most natural extension of General Relativity and it attracted interest over the years in view of its link with fundamental properties of particle motion. The bulk of the approaches concerning the torsion dynamics…