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

We introduce a new interacting particle model with blocking and pushing interactions. Particles evolve on a"currency sign(+) jumping on their own volition rightwards or leftwards according to geometric jumps with parameter qa(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).