Related papers: Brownian motion and affine Kac-Moody algebras

- Synth\`ese des travaux pr\'esent\'es en vue d'une Habilitation \`a Diriger des Recherches - Synthesis of works presented towards the Habilitation degree This is a summary (in French) of my work in number theory, group theory and…

This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with…

The main purpose of this work is to review the results obtained recently concerning the unitarization of highest weight representations for affine Kac-Moody algebras following the work of Jakobsen and Kac.

This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.

This is the text of the Hermann Weyl Prize lecture given by the author at the XXIV Colloquium on Group Theoretical Methods in Physics, Paris, July 2002 (to appear in the Proceedings of the Colloquium).

The paper is a short survey of recent developments in the area of word maps evaluated on groups and algebras. It is aimed to pose questions relevant to Kac--Moody theory.

The method of graded contractions, based on the preservation of the automorphisms of finite order, is applied to the affine Kac-Moody algebras and their representations, to yield a new class of infinite dimensional Lie algebras and…

A graduate level textbook on the interplay between complex analysis and Brownian motion.

This paper is a review of the recent progresses on the branching brownian motion seen from its left-most particule. We describe in particular the recent works by Arguin-Bovier-Kistler and A\"id\'ekon-Berestycki-Brunet-Shi. This is the text…

We outline a new approach to classify real forms and automorphisms of finite order of affine Kac-Moody algebras.

In this thesis, we consider several aspects of over-extended and very-extended Kac-Moody algebras in relation with theories of gravity coupled to matter. In the first part, we focus on the occurrence of KM algebras in the cosmological…

We construct Brownian motion on a wide class of metric spaces similar to graphs, and show that its cover time admits an upper bound depending only on the length of the space.

The role of Kac-Moody algebras in exploiting symmetries of particle physics and string theory is described.

This is an extended version of the lecture notes to a mini-course devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop.

We extend results for the K-theory of Hecke algebras of reductive $p$-adic groups to completed Kac-Moody groups.

We provide some necessary details to several arguments appearing in our previous paper ``Canonical bases for quantum generalized Kac-Moody algebras''. We also make the link with some other work on the same subject.

We solve the problem of formulating Brownian motion in a relativistically covariant framework in 1+1 and 3+1 dimensions. We obtain covariant Fokker-Planck equations with (for the isotropic case) a differential operator of invariant…

We construct a sequence of Markov processes on the set of dominant weights of the Affine Lie algebra $\hat{\mathfrak{sl}_2}(\C)$ which involves tensor product of irreducible highest weight modules of $\hat{\mathfrak{sl}_2}(\C)$ and show…

The aim of this paper is to remember and review several exceptional investigations on the theory of the Brownian motion. Although in these works the first correct hydrodynamic theories of the translational and rotational Brownian motion…

The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. We use Dirichlet form methods to construct…