Riemann-Hilbert approach to multi-time processes; the Airy and the   Pearcey case
  We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov (IIKS) and hence related to suitable Riemann-Hilbert problems, thus extending the known results for the single-time case. We focus on the Airy and Pearcey processes. As an example of applications we re-deduce a third order PDE, found by Adler and van Moerbeke, for the two-time Airy process. 
M. Bertola and M. Cafasso
math-ph math.MP math.PR nlin.SI