Decision making times in mean-field dynamic Ising model

TL;DR

This paper analyzes the time it takes for a mean-field Ising model to transition from an unstable to a stable state, providing a limit theorem for the decision time distribution in large systems.

Contribution

It introduces a limit theorem describing the distribution of decision times in a low-temperature mean-field Ising model near the critical point.

Findings

Derived a limit distribution for decision times in the model

Characterized the exit time behavior near the unstable equilibrium

Provided insights into phase transition dynamics in mean-field models

Abstract

We consider a dynamic mean-field ferromagnetic model in the low-temperature regime in the neighborhood of the zero magnetization state. We study the random time it takes for the system to make a decision, i.e., to exit the neighborhood of the unstable equilibrium and approach one of the two stable equilibrium points. We prove a limit theorem for the distribution of this random time in the thermodynamic limit.