HET Seminar | Henry Lin, Princeton University | "Solving Random Matrix Models with Positivity” | via ZOOM

Fri, Mar 27, 2020, 1:45 pm

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A new approach to solving random matrix models directly in the
large N limit is developed. First, a set of numerical values for some
low-pt correlation functions is guessed. The large N loop equations are
then used to generate values of higher-pt correlation functions based on
this guess. Then one tests whether these higher-pt functions are
consistent with positivity requirements, e.g., tr M^{2k} > 0. If not,
the guessed values are systematically ruled out. In this way, one can
constrain the correlation functions of random matrices to a tiny
subregion which contains (and perhaps converges to) the true solution.
This approach is tested on single and multi-matrix models and handily
reproduces known solutions. It also produces strong results for
multi-matrix models which are not believed to be solvable. A tantalizing
possibility is that this method could be used to search for new critical
points, or string worldsheet theories.

via Zoom