2012/03/28 by David B. Saakian
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Artificial intelligence #Class (philosophy) #Complex Systems and Time Series Analysis #Computer science #Fractal #Markov chain #Mathematical analysis #Mathematics #Multifractal system #Physics #Random walk #Space (punctuation) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.85.031142
published as Phys. Rev. E, Phys. Rev. E, v. 85, 031142 (2012)
openalex publication_date 2012/03/28 · arxiv created 2012/12/04 · arxiv updated 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We map the Markov-switching multifractal model (MSM) onto the random energy model (REM). The MSM is, like the REM, an exactly solvable model in one-dimensional space with nontrivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multifractal behavior. We also introduce the continuous branching version of the model, calculate the moments, and prove multiscaling behavior. Different phases have different multiscaling properties.