The \(3x +1\) problem: Two stochastic models

DOI10.1214/aoap/1177005779zbMath0742.60027OpenAlexW1991036063MaRDI QIDQ1186306

Alan Weiss, Jeffrey C. Lagarias

Publication date: 28 June 1992

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1177005779

zbMATH Keywords

large deviationsstochastic modelsfamily of branching random walks

Mathematics Subject Classification ID

Applications of branching processes (60J85) Large deviations (60F10) Iteration of real functions in one variable (26A18) Elementary number theory (11A99)

Related Items (12)

Lower bounds for the total stopping time of 3𝑥+1 iterates ⋮ Statistical properties of an iterated arithmetic mapping ⋮ Greedy Search on the Binary Tree with Random Edge-Weights ⋮ A randomized version of the Collatz \(3x + 1\) problem ⋮ The Distribution of 3x+1 Trees ⋮ The \(3x+1\) problem: a lower bound hypothesis ⋮ A probabilistic model for the 5\(x\)+1 problem and related maps ⋮ Multiplication algorithm based on Collatz function ⋮ The Collatz conjecture and the quantum mechanical harmonic oscillator ⋮ Maximum excursion and stopping time record-holders for the problem: Computational results ⋮ Embedding the 3x + 1 Conjecture in a 3x + d Context ⋮ Almost all orbits of the Collatz map attain almost bounded values

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