Related papers: Markov paths, loops and fields

The main topic of these notes are Markov loops, studied in the context of continuous time Markov chains on discrete state spaces. We refer to [1] and [2] for the short "history" of the subject. In contrast with these references, symmetry is…

We investigate the relations between the Poissonnian loop ensembles , their occupation fields, non ramified Galois coverings of a graph, the associated gauge fields, and random Eulerian networks.

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 purpose of this note is to explore some simple relations between loop measures, determinants, and Gaussian Markov fields.

This is a survey of various types of Floer theories (both in symplectic geometry and gauge theory) and relations among them.

Since the work of Lawler and Werner on "loop soups", these ensembles have also been the object of many investigations. Their properties can be studied in the context of rather general Markov processes, in particular Markov chains on graphs.…

We introduce "book links" as a generalization of braids in open book decompositions; this new class of objects includes both braids and plats as special cases. We then prove a version of Markov's theorem in this general setting by extending…

In this review-type paper written at the occasion of the Oberwolfach workshop {\em One-sided vs. Two-sided stochastic processes} (february 22-29, 2020), we discuss and compare Markov properties and generalisations thereof in more…

We discuss a couple of examples of Markov chains. This note is written primarily for school students; it is based on a lecture given by the first author at a Math Circle at NAS (www.assagames.com/nas).

We investigate random Eulerian networks defined by Markov loops and the associated fields, flows and maps.

We describe simple properties of some soups of unoriented Markov loops and of some soups of oriented Markov loops that can be interpreted as a spatial Markov property of these loop-soups. This property of the latter soup is related to…

This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by…

This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories and give some examples which illustrate a somewhat mysterious correspondence…

These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…

These lecture notes are a friendly introduction to monopole Floer homology. We discuss the relevant differential geometry and Morse theory involved in the definition. After developing the relation with the four-dimensional theory, our…

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

These are lecture notes of the 48th Saint-Flour summer school, July 2018, on the topic of planar maps, random walks and the circle packing theorem.

This is a concise survey of links between Galois module theory and class field theory (CFT). It explores various uses of CFT in Galois module theory, it comments on the absence of CFT in contexts where it might be expected to play a role…

A non-symplectic generalization of Hamiltonian mechanics is considered. It allows include into consideration "non-Lagrange" systems, such as theory of charged particle in the field of magnetic monopole. The corresponding generalization for…

In these mostly expository lectures, we give an elementary introduction to conformal field theory in the context of probability theory and complex analysis. We consider statistical fields, and define Ward functionals in terms of their Lie…