Asymptotics of the tacnode process: a transition between the gap probabilities from the tacnode to the Airy process. (English) Zbl 1305.60073
Summary: We study the gap probabilities of the single-time tacnode process. Through steepest descent analysis of a suitable Riemann-Hilbert problem, we show that under appropriate scaling regimes the gap probability of the tacnode process degenerates into a product of two independent gap probabilities of the Airy processes.
MSC:
| 60J60 | Diffusion processes |
| 60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 34M60 | Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) |
