Random vector and matrix and vector theories: a renormalization group approach

Understand

Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter.

• This has generated a tremendous expansion of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly.
• However, the somewhat paradoxical situation is that either models can be solved exactly or little can be said.
• Since the solved models display critical points and universal properties, it is tempting to use renormalization group ideas to determine universal properties, without solving models explicitly.