The random interchange process on the hypercube

TL;DR

This paper proves that in the random interchange process on the hypercube, a phase transition occurs with the formation of very long cycles, indicating a significant change in the system's structure.

Contribution

It establishes the occurrence of a phase transition and the emergence of long cycles in the random interchange process on the hypercube, a new result in this context.

Findings

Phase transition occurs in the process

Emergence of diverging cycle lengths

Structural change in the hypercube model

Abstract

We prove the occurrence of a phase transition accompanied by the emergence of cycles of diverging lengths in the random interchange process on the hypercube.