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