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).
Interacting particle model Random matrices Random tiling Representation theory
Mathematics Subject Classification
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The author would like to thank Alexei Borodin for his suggestions and helpful explanations.
Borodin, A., Kuan, J.: Random surface growth with a wall and Plancherel measures for O(∞). Commun. Pure Appl. Math. 67, 831–894 (2010)
Borodin, A., Ferrari, P.: Anisotropic growth of random surfaces in 2+1 dimensions (2008). arXiv:0804.3035v2