We obtain a formula for the -dimensional distributions of the process in terms of a Fredholm determinant on , as opposed to the standard formula which involves extended kernels, on . The formula is analogous to an earlier formula of Prahofer and Spohn (J Stat Phys 108(5-6):1071-1106, 2002) for the process. Using this formula we are able to prove that the process is Holder continuous with exponent -and that it fluctuates locally like a Brownian motion. We also explain how the same methods can be used to obtain the analogous results for the process. As a consequence of these two results, we derive a formula for the continuum statistics of the process, analogous to that obtained in Corwin et al. (Commun Math Phys 2011, to appear) for the process.