Journal of Theoretical Probability

, Volume 26, Issue 2, pp 568–588 | Cite as

An Interacting Particle Model and a Pieri-Type Formula for the Orthogonal Group

Article

Abstract

We introduce a new interacting particle model with blocking and pushing interactions. Particles evolve on ℤ+ jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q∈(0,1). We show that the model involves a Pieri-type formula for the orthogonal group. We prove that the two extreme cases—q=0 and q=1—lead, respectively, to the random tiling model studied in Borodin and Kuan (Commun. Pure Appl. Math. 67:831–894, 2010) and the random matrix model considered in forthcoming paper of Defosseux (Electr. Commun. Probab., 2012).

Keywords

Interacting particle model Random matrices Random tiling Representation theory 

Mathematics Subject Classification

60J10 17B10 

Notes

Acknowledgements

The author would like to thank Alexei Borodin for his suggestions and helpful explanations.

References

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Appliquées à Paris 5Université Paris 5Paris Cedex 06France

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