Factorized Duality, Stationary Product Measures and Generating Functions

Frank Redig, Federico Sau

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
27 Downloads (Pure)


We find all self-duality functions of the form (Formula presented.)for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as duality and self-duality functions for their continuous counterparts. The approach is based on, firstly, a general relation between factorized duality functions and stationary product measures and, secondly, an intertwining relation provided by generating functions. For the interacting particle systems, these self-duality and duality functions turn out to be generalizations of those previously obtained in Giardinà et al. (J Stat Phys 135:25–55, 2009) and, more recently, in Franceschini and Giardinà (Preprint, arXiv:1701.09115, 2016) . Thus, we discover that only these two families of dualities cover all possible cases. Moreover, the same method discloses all simple factorized self-duality functions for interacting diffusion systems such as the Brownian energy process, where both the process and its dual are in continuous variables.

Original languageEnglish
Pages (from-to)980-1008
Number of pages29
JournalJournal of Statistical Physics
Issue number4
Publication statusPublished - 2018


  • Duality
  • Generating function
  • Interacting particle systems
  • Intertwining
  • Orthogonal polynomials


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