An interacting particle model and a Pieri-type formula for the orthogonal group

TL;DR

This paper introduces a new interacting particle model with blocking and pushing, revealing connections to Pieri-type formulas for the orthogonal group and linking to random tiling and matrix models at extreme parameters.

Contribution

It presents a novel particle interaction model that relates to algebraic formulas for the orthogonal group and connects to existing random tiling and matrix models.

Findings

Model involves a Pieri-type formula for the orthogonal group.

Extreme cases q=0 and q=1 correspond to known tiling and matrix models.

The model generalizes and unifies different probabilistic models.

Abstract

We introduce a new interacting particles model with blocking and pushing interactions. Particles evolve on the positive line jumping on their own volition rightwards or leftwards according to geometric jumps with parameter q. 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 a random tiling model studied by Borodin and Kuan and to a random matrix model.