Hard-edge asymptotics of the Jacobi growth process

We introduce a two parameter (a,β > -1) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials {P(a,β)k } k=0. The family includes previously discovered Plancherel measures for the infinite-dimensional orthogonal and symplectic groups. The construction uses certain multivariate BC-type orthogonal polynomials that generalize the characters of these groups. The local asymptotics near the hard edge where one expects distinguishing behavior yields the multi-time (a,β)-dependent discrete Jacobi kernel and the multi-time β-dependent hard-edge Pearcey kernel. The hard-edge Pearcey kernel has previously appeared in the asymptotics of non-intersecting squared Bessel paths at the hard edge.