The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
Bootstrapping Matrix Quantum Mechanics,
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Fractional operator powers generate non-positivity constraints that determine the SYK bilinear spectrum and converge to exact eigenvalues under truncation.
A bootstrap method using density-matrix positivity and steady-state conditions produces bounds on steady-state expectation values, the critical coupling, and the Liouvillian gap for the quantum contact process.
Finite-N bootstrap yields N-independent bounds for matrix models but N-dependent novel bounds on the two-point function versus quartic coupling for tensor models.
Derives explicit recursion relations for Puiseux expansion coefficients in non-Hermitian perturbation theory at exceptional points of order N, with two equivalent forms for the first two eigenvalue corrections.
Bootstrap method in quantum mechanics has an ambiguity problem for mixed potential and operator types, with three proposed resolutions.
A regularized finite-dimensional master field numerically solves large-N reduced matrix models, reproducing exact Euclidean solutions and perturbative Minkowski results for one- and two-matrix cases.