Consistent particle systems and duality

Carinci, Gioia; Giardinà, Cristian; Redig, F.H.J.

doi:10.1214/21-EJP684

Consistent particle systems and duality

Title

Consistent particle systems and duality

Author

Carinci, Gioia (Università Degli Studi di Modena e Reggio Emilia)
Giardinà, Cristian (Università Degli Studi di Modena e Reggio Emilia)
Redig, F.H.J. (TU Delft Applied Probability)

Date

2021

Abstract

We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the Kipnis-Marchioro-Presutti model. Consistent systems are such that the distribution obtained by first evolving n particles and then removing a particle at random is the same as the one given by a random removal of a particle at the initial time followed by evolution of the remaining n − 1 particles. In this paper we discuss two main results. Firstly, we show that, for reversible systems, the property of consistency is equivalent to self-duality, thus obtaining a novel probabilistic interpretation of the self-duality property. Secondly, we show that consistent particle systems satisfy a set of recursive equations. This recursions implies that factorial moments of a system with n particles are linked to those of a system with n − 1 particles, thus providing substantial information to study the dynamics. In particular, for a consistent system with absorption, the particle absorption probabilities satisfy universal recurrence relations. Since particle systems with absorption are often dual to boundary-driven non-equilibrium systems, the consistency property implies recurrence relations for expec-tations of correlations in non-equilibrium steady states. We illustrate these relations with several examples.

Subject

Boundary driven systems
Duality
Interacting particle systems
Non-equilibrium stationary measure
Symmetric exclusion process
Symmetric inclusion process

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http://resolver.tudelft.nl/uuid:d458468a-2b60-48db-a7a4-8321577a2836

DOI

https://doi.org/10.1214/21-EJP684

ISSN

1083-6489

Source

Electronic Journal of Probability, 26, 1-31

Part of collection

Institutional Repository