Related papers: Markov loops, determinants and Gaussian fields
The aim of this note is to construct a probability measure on the space of trajectories in a continuous time Markov chain having a finite state diagram, or more generally which admits a global bound on its degree and rates. Our approach is…
We prove the equivalence of the local property for an irreducible regular Dirichlet form and the Markov property for the Gaussian field associated with the Dirichlet form. Moreover we introduce a strong Markov property for Gaussian fields…
The article is devoted to a new type of measures which are hypercomplex generalizations of Gaussian-type measures. The considered such measures are related with solutions of high order hyperbolic PDEs and related Markov processes. Their…
We provide a systematic study of the notion of duality of Markov processes with respect to a function. We discuss the relation of this notion with duality with respect to a measure as studied in Markov process theory and potential theory…
The aim of this paper is to provide Markov-type inequalities in the setting of weighted Sobolev spaces when the considered weights are generalized classical weights. Also, as results of independent interest, some basic facts about Sobolev…
The purpose of this short communication is to make some observations on the connections between various existing formulas of counting the number of sublattices of a fixed index in an $n$-dimensional lattice and their connection with the…
In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations.
We study the complex free field associated with a symmetric Markov chain. Applications are given to loop ensembles, second Ray Knight theorem and random Eulerian circuits.
The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we prove a conjecture concerning the minimality of…
We discuss several similarities and differences between the concepts of electric and magnetic dipoles. We then consider the relation between the magnetic dipole and a current loop and show that in the limit of a pointlike circuit, their…
We apply the general conception of non-Abelian gauge fields for description of magnetic soliton excitations. We show that the component of the gauge field along the soliton local magnetization (Abelian part of the gauge potential)…
A method is proposed that allows one to infer the sum of the values of an observable taken during contacts with a pointer state. Hereby the state of the pointer is updated while contacted with the system and remains unchanged between…
This paper specifies a notation for Markov decision processes.
A discrete field formalism exposes the physical meaning and origins of gauge fields, their symmetries and singularities. They represent a lack of a stricter field-source coherence.
Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are…
We study the structure of quantum Markov Processes from the point of view of product systems and their representations.
Exact relations between gauge-invariant vacuum correlators in QCD are derived. Derivatives of the correlators are expressed in terms of higher orders correlators. The behaviour of the correlators at large and small distances due to these…
We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…