2025/09/07 by Uri Gabor, Gabor, Uri
Mathematics · #37A35 #37A50 #60G10 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Dynamics and Fractals #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2509.06018
openalex publication_date 2025/09/07 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
The problem of what moments can exist for the coding radius of a finitary map between two i.i.d. processes, has been extensively studied in the case of ℤ-processes. Here we treat this problem for factor maps between ℤd-processes (d>1). By modeling the homomorphism with a map between spaces of finite sequences, we extend Harvey and Peres' result, showing that for a finitary homomorphism between two i.i.d. processes of equal entropy, if the coding radius of the map has a finite (d)/(2)-moment, then the two processes share the same informational variance. We use our modeling technique to prove a "Schmidt-type theorem" - that in case the above homomorphism has a coding radius of exponential tails, then the two processes are essentially the same. This result appears to be new even for the one-dimensional case, addressing a question of Angel and Spinka.