Related papers: Markov loops, determinants and Gaussian fields
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…
We give an explicit formula for the determinant of the Gau{\ss}-Manin connection for an irregular connection on a Zariski open set of the projective line $\P^1_K$ over a function field $K$ over a field $k$ of characteristic zero.
This survey discusses the classical Bernstein and Markov inequalities for the derivatives of polynomials, as well as some of their extensions to general sets.
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.
Magnetic interaction between a weighing sample and an external magnetic field allows to measure characteristics of magnetic field (a sample with known magnetic characteristics), as well as the magnetic properties of a sample (a known…
A formula expressing the fermionic determinant as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and are indexed by loops of…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
Some unusual relations between stress tensors, conservation and equations of motion are briefly reviewed.
A linear map between two vector spaces has a very important characteristic: a determinant. In modern theory two generalizations of linear maps are intensively used: to linear complexes (the nilpotent chains of linear maps) and to non-linear…
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
These are notes based on a course that I gave at the University of Chicago in Fall 2016 on "Loop measures and the loop-erased random walk." This is not intended to be a comprehensive view but rather a personal selection of some key ideas…
This Dissertation collects my results on the interpretation, characterization, quantification and application of bipartite and multipartite entanglement in Gaussian states of continuous variable systems.
The aim of this text is to establish some relations between Markov chains in Dirichlet Environments on directed graphs and certain hypergeometric integrals associated with a particular arrangement of hyperplanes. We deduce from these…
This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…
The electromagnetic measurements of general relativistic gravitomagnetic effects which can be performed within a conductor embedded in the space-time of slow rotating gravitational object in the presence of magnetic field are proposed.
We introduce an equation named matrix Dirac equation which can be considered as a generalization of Dirac equation for an electron. The liaison between matrix Dirac equation and standard Dirac equation is discussed. We write a lagrangian…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…