The Markov Switching Multi-fractal models as a new class of REM-like models in 1-dimensional space

TL;DR

This paper maps the Markov Switching Multi-fractal model onto the Random Energy Model, revealing four possible phases with distinct multiscaling behaviors in 1D, and introduces a continuous branching version with analytical results.

Contribution

It introduces a novel mapping of MSM onto REM, explores phase behavior in multi-fractal random walks, and develops a continuous branching version with analytical insights.

Findings

Four distinct statistical physics phases identified.

Multiscaling behavior varies across phases.

Continuous branching MSM model analyzed and characterized.

Abstract

We map the Markov Switching Multi-fractal model (MSM) onto the Random Energy Model (REM). The MSM is, like the REM, an exactly solvable model in 1-d space with non-trivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multi-fractal behavior. We also introduce the continuous branching version of the model, calculate the moments and prove multiscaling behavior. Different phases have different multi-scaling properties.