Large-N dynamics of the spiked tensor model with random initial conditions

TL;DR

This paper develops a path integral framework to analyze the large-N dynamics of the spiked tensor model with random initial conditions, revealing that melonic diagrams dominate the saddle point equations.

Contribution

It introduces a novel path integral approach to study the dynamics of the spiked tensor model at large N, highlighting the dominance of melonic diagrams.

Findings

Melonic diagrams dominate the saddle point equations.

Path integral method effectively analyzes large-N dynamics.

Provides insights into the behavior of the spiked tensor model.

Abstract

In these notes, we develop a path integral approach for the partial differential equations with random initial conditions. Then, we apply it to the dynamics of the spiked tensor model and show that the large-$N$ saddle point equations are dominated by the melonic type diagrams.