Eigenvalue distribution from bootstrap estimates

The bootstrap method has proven useful for a wide range of matrix models. Here, we show that the computed momenta can be used to reconstruct the underlying eigenvalue probability distribution, which in turn allows us to compute the free energy of the model, a necessary quantity for identifying the thermodynamically preferred solution. We verify the method on the well-studied quartic potential model and then apply it to a recently analysed asymmetric multi-trace model. We consider an extended class of possible solutions and demonstrate that free-energy analysis reliably selects the correct one, making it an essential tool for studying models with a complex solution structure.