The affine Lie algebra \mathfraksl₂(\C) and a conditioned space-time Brownian motion

2014/01/14 by Manon Defosseux, Defosseux, Manon · 1 citation
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1401.3115

openalex publication_date 2014/01/14 · arxiv created 2014/06/02 · arxiv updated 2014/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a sequence of Markov processes on the set of dominant weights of the Affine Lie algebra \mathfraksl₂(\C) which involves tensor product of irreducible highest weight modules of \mathfraksl₂(\C) and show that it converges towards a Doob's space-time harmonic transformation of a space-time Brownian motion.

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