Genealogies of Interacting Particle Systems

0534685 - ÚTIA 2021 RIV SG eng M - Monography Chapter
Sturm, A. - Swart, Jan M. - Völlering, F.
The Algebraic Approach to Duality: An Introduction.
New Jersey: Hackensack: World Scientific, 2020. Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore, 38. ISBN 978-981-12-0608-5; ISBN 978-981-12-0610-8. ISSN 1793-0758. In: Genealogies of Interacting Particle Systems. Singapure: World Scientific, 2020, s. 81-150. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, 38. ISBN 978-981-120-608-5
R&D Projects: GA ČR(CZ) GA16-15238S
Institutional support: RVO:67985556
Keywords : interacting particle system * duality * intertwining * representations of Lie algebras
OECD category: Statistics and probability
http://library.utia.cas.cz/separaty/2020/SI/swart-0534685.pdf

This survey article gives an elementary introduction to the algebraic approach to Markov process duality, as opposed to the pathwise ap- proach. In the algebraic approach, a Markov generator is written as the sum of products of simpler operators, which each have a dual with respect to some duality function. We discuss at length the recent sug- gestion by Giardinà, Redig, and others, that it may be a good idea to choose these simpler operators in such a way that they form an irreducible representation of some known Lie algebra. In particular, we collect the necessary background on representations of Lie algebras that is crucial for this approach. We also discuss older work by Lloyd and Sudbury on duality functions of product form and the relation between intertwining and duality.
Permanent Link: http://hdl.handle.net/11104/0313197