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We express the gap probabilities of the tacnode process as the ratio of twoFredholm determinants; the denominator is the standard Tracy-Widomdistribution, while the numerator is the Fredholm determinant of a veryexplicit kernel constructed with Airy functions and exponentials. The formulaallows us to apply the theory of numerical evaluation of Fredholm determinantsand thus produce numerical results for the gap probabilities. In particular weinvestigate numerically how, in different regimes, the Pearcey processdegenerates to the Airy one, and the tacnode degenerates to the Pearcey andAiry ones.

The gap probabilities of the tacnode, Pearcey and Airy point processes, their mutual relationship and evaluation