Entangled random pure states with orthogonal symmetry: exact results

We compute analytically the density rhovN,M(λ) of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average Renyi entropy for reduced density matrices of entangled random pure states with orthogonal symmetry (β = 1). The results are valid for arbitrary dimensions N = 2k, M of the corresponding Hilbert space partitions, and are in excellent agreement with numerical simulations.