The Algebraic Approach to Duality: An Introduction

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00534685" target="_blank" >RIV/67985556:_____/20:00534685 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/9789811206092_0003" target="_blank" >http://dx.doi.org/10.1142/9789811206092_0003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/9789811206092_0003" target="_blank" >10.1142/9789811206092_0003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Algebraic Approach to Duality: An Introduction

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The Algebraic Approach to Duality: An Introduction

Popis výsledku anglicky

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.

Druh

C - Kapitola v odborné knize

CEP obor

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OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA16-15238S" target="_blank" >GA16-15238S: Kolektivní chování velkých stochastických systémů</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Genealogies of Interacting Particle Systems

ISBN

978-981-120-608-5

Počet stran výsledku

69

Strana od-do

81-150

Počet stran knihy

364

Název nakladatele

World Scientific

Místo vydání

Singapure

Kód UT WoS kapitoly

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