2022/02/08 by Anton A. Kutsenko, Kutsenko, Anton A
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2202.04032
openalex publication_date 2022/02/08 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Exponential stochastic compression is the process when every second cell of an infinite chain may increase its weight merging randomly with left, right, or both neighboring cells. The total mass conservation is assumed. After that, merged cells fill the empty space, compressing the chain twice. They may fill empty spaces in two different ways: (I) using shifts only, i.e. preserving the order; (II) using shifts and random permutations. Compressing the initial homogeneous chain with cell weights 1 many times, we compute final densities ρi of cells with weight i=1,2,3,.... The main result is that ρi/ρ1=i in the ordered case (I), and ρi/ρ1≈1.464910...(i-1/4) in the disordered case (II). The multiplier in the disordered case has a fractal nature. The compression of initially inhomogeneous chains and rescaled continuous densities are also discussed.