The exact FZZT brane partition function for topological gravity with matter is computed using the dual two-matrix model. We show how the effective theory of open strings on a stack of FZZT branes is described by the generalized Kontsevich matrix integral, extending the earlier result for pure topological gravity. Using the well-known relation between the Kontsevich integral and a certain shift ...

We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N≤M, a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Sch...

We consider the reduced density matrix $\rho_{A}^{(m)}$ of a bipartite system $AB$ dimensionality $mn$ in Gaussian ensemble random, complex pure states composite system. For given $m$ subsystem $A$, eigenvalues $\lambda_{1}^{(m)},\ldots, \lambda_{m}^{(m)}$ are correlated random variables because their sum equals unity. The following quantities known, among others: joint probability function (PD...