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Finite-State Markov Chains Obey Benford’S Law, Arno Berger, Theodore P. Hill, Bahar Kaynar, Ad Ridder
Finite-State Markov Chains Obey Benford’S Law, Arno Berger, Theodore P. Hill, Bahar Kaynar, Ad Ridder
Theodore P. Hill
A sequence of real numbers (xn) is Benford if the significands, i.e., the fraction parts in the floating-point representation of (xn), are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain with transition probability matrix P and limiting matrix P* is Benford if every component of both sequences of matrices (Pn−P*) and (Pn+1−Pn) is Benford or eventually zero. Using recent tools that established Benford behavior for finite-dimensional linear maps, via the classical theories of uniform distribution modulo 1 and Perron–Frobenius, this paper derives a simple sufficient condition (“nonresonance”) guaranteeing that P, or the Markov chain associated with it, …
Benford’S Law Strikes Back: No Simple Explanation In Sight For Mathematical Gem, Arno Berger, Theodore P. Hill
Benford’S Law Strikes Back: No Simple Explanation In Sight For Mathematical Gem, Arno Berger, Theodore P. Hill
Theodore P. Hill
No abstract provided.