Duality for Markov Processes

Cristian Giardinà is a professor of mathematics at Modena and Reggio Emilia University. His research activity centers on probability theory, statistical physics, and interacting particle systems. He has been working on duality properties of Markov processes, the hydrodynamic limit of open systems, large deviations and cloning algorithms, and the Ising model on random graphs. The overall aim is to understand how complex macroscopic behavior arises from microscopic models. He has published over 90 scientific papers, and two monographs on “Free boundary problems in PDE and particle systems” and “Perspectives on spin glasses”. Frank Redig is a professor of probability theory at the Delft Institute of Applied Mathematics. His research focuses on Markov process theory, Gibbs measures, non-equilibrium statistical physics, and interacting particle systems.

• Chapter 1. Introduction.- Chapter 2. Basics of the algebraic approach.- Chapter 3. Duality for independent random walkers: part 1.- Chapter 4. Duality for independent random walkers: part 2.- Chapter 5. Duality for the symmetric inclusion process.- Chapter 6. Duality for the Brownian energy process.- Chapter 7. Duality for the symmetric partial exclusion process.- Chapter 8. Duality for other models.- Chapter 9. Orthogonal dualities.- Chapter 10. Consistency.- Chapter 11. Duality for non-equilibrium systems.- Chapter 12. Duality and macroscopic fields.- Chapter 13. Duality and integrable models.

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