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We study the gap probabilities of the single-time Tacnode process. Throughsteepest descent analysis of a suitable Riemann-Hilbert problem, we show thatunder appropriate scaling regimes the gap probability of the Tacnode processdegenerates into a product of two independent gap probabilities of the Airyprocesses.

Asymptotics of the Tacnode process: a transition between the gap probabilities from the Tacnode to the Airy process