Joint eigenvector distributions of symmetric random tensors are computed via QFT methods, yielding random matrix forms and universal large-dimension asymptotics governed by tensor geometries.
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Order parameters for unitary ensembles solve the modified KP equation via the Volterra lattice while orthogonal ensembles yield a new integrable chain via the Pfaff lattice, with thermodynamic limits being hydrodynamic-type systems solved by the same semi-discrete dynamical chain.
The free energy of a D-dimensional matrix model on a curved background is the Einstein-Hilbert action with cosmological constant, where the constants are expectation values of graph invariants from ribbon graphs.
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Joint distributions of eigenvectors of symmetric random tensors
Joint eigenvector distributions of symmetric random tensors are computed via QFT methods, yielding random matrix forms and universal large-dimension asymptotics governed by tensor geometries.
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Random matrix ensembles and integrable differential identities
Order parameters for unitary ensembles solve the modified KP equation via the Volterra lattice while orthogonal ensembles yield a new integrable chain via the Pfaff lattice, with thermodynamic limits being hydrodynamic-type systems solved by the same semi-discrete dynamical chain.
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From Matrix Models to Gaussian Molecules and the Einstein-Hilbert Action
The free energy of a D-dimensional matrix model on a curved background is the Einstein-Hilbert action with cosmological constant, where the constants are expectation values of graph invariants from ribbon graphs.