The KPZ equation and moments of random matrices

Abstract

The logarithm of the diagonal matrix element of a high power of a random matrix converges to the Cole-Hopf solution of the Kardar-Parisi-Zhang equation in the sense of one-point distributions.

10pp; fixed typos in eq. (1.2) and Rmk. 1.2

References in corpus (6)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation and its universality class
• The KPZ Limit of ASEP with Boundary
• Stochastic six-vertex model in a half-quadrant and half-line open ASEP
• Moments Match between the KPZ Equation and the Airy Point Process
• On the edge universality of the local eigenvalue statistics of matrix models

Cited by in corpus (3)

• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Moments of the SHE under delta initial measure
• The Tracy-Widom distribution at large Dyson index