1 citations · 4 across the 9 of their papers we have counts for
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Multiplicative Turing Ensembles, Pareto's Law, and Creativity
Alexander Kolpakov, Aidan Rocke
We study integer-valued multiplicative dynamics driven by i.i.d. prime multipliers and connect their macroscopic statistics to universal codelengths. We introduce the Multiplicativ…
Lagrangians, Renormalization, and Quantization in Prefix Coding
Alexander Kolpakov, Aidan Rocke
We develop a statistical mechanics framework for prefix coding based on variational principles, renormalization, and quantization. A Lagrangian formulation of entropy-optimal encod…
Benford's Law from Turing Ensembles and Integer Partitions
Alexander Kolpakov, Aidan Rocke
We develop two complementary generative mechanisms that explain when and why Benford's first-digit law arises. First, a probabilistic Turing machine (PTM) ensemble induces a geomet…
Machine Learning of the Prime Distribution
Alexander Kolpakov, Aidan Rocke
In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a…
An information-theoretic proof of the Erdős-Kac theorem
Aidan Rocke
In this article we show that the Erdős-Kac theorem, which informally states that the number of prime divisors of very large integers converges to a normal distribution, has an eleg…