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We prove that matrix Fredholm determinants related to multi-time processescan be expressed in terms of determinants of integrable kernels \`a laIts-Izergin-Korepin-Slavnov (IIKS) and hence related to suitableRiemann-Hilbert problems, thus extending the known results for the single-timecase. We focus on the Airy and Pearcey processes. As an example of applicationswe re-deduce a third order PDE, found by Adler and van Moerbeke, for thetwo-time Airy process.

Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case