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arXiv · 2609.37020

On random Binomial-Fibonacci sequences

Bernard Bercu·Fabrice Gamboa
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Abstract

Motivated by the pioneer work of Viswanath \cite{VIS2000} on random Fibonacci sequences and the development of random Euclidean addition chains in cryptography, we introduce a new family of random Binomial-Fibonacci sequences. We study the asymptotic behavior of their finite-time Lyapunov exponents. In the special case of random Bernoulli-Fibonacci sequences, we show that they convergence almost surely to an explicit Lyapunov exponent and prove a central limit theorem with an explicit formula for the variance. We also show that they satisfy a large deviation principle.

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Bernard Bercu, Fabrice Gamboa. 2026-09-29. On random Binomial-Fibonacci sequences. https://arxiv.org/abs/2609.37020

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