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
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