Hard-edge asymptotics of the Jacobi growth process

Abstract

We introduce a two parameter ($\alpha ,\beta >-1$) family of interacting particle systems with determinantal correlation kernels expressible in terms of Jacobi polynomials $\{P_k^{(\alpha ,\beta )}{\}}_{k\ge 0}$. 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 $(\alpha ,\beta )$-dependent discrete Jacobi kernel and the multi-time $\beta$-dependent hard-edge Pearcey kernel. For nonnegative integer values of $\beta$, the hard-edge Pearcey kernel had previously appeared in the asymptotics of non-intersecting squared Bessel paths at the hard edge.

this article supersedes arXiv:1506.08742

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• Large Complex Correlated Wishart Matrices: The Pearcey Kernel and Expansion at the Hard Edge
• The hard edge tacnode process and the hard edge Pearcey process with non-intersecting squared Bessel paths
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Cited by in corpus (1)

• Nonintersecting Brownian bridges between reflecting or absorbing walls