Stochastic Duality and Orthogonal Polynomials

  • Chiara Franceschini
  • Cristian GiardinàEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 300)


For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal polynomial) can be studied via expectations with respect to the dual process (which evolves the index of the polynomial). The set of processes include interacting particle systems, such as the exclusion process, the inclusion process and independent random walkers, as well as interacting diffusions and redistribution models of Kipnis–Marchioro–Presutti type. Duality functions are given in terms of classical orthogonal polynomials, both of discrete and continuous variable, and the measure in the orthogonality relation coincides with the process stationary measure.


Interacting particle systems Duality Orthogonal polynomials Exclusion process 



This research was supported by the Italian Research Funding Agency (MIUR) through FIRB project grant no. RBFR10N90W and in part by the National Science Foundation under Grant No. NSF PHY11-25915. We acknowledge a useful discussion on the topic of this paper with Cédric Bernardin during the trimester “Disordered systems, random spatial processes and their applications” that was held at the Institute Henri Poincaré.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  2. 2.University of Modena and Reggio EmiliaModenaItaly

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