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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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Cite

BibTeXRIS
BibTeX
@misc{bercu2026random,
  title = {{On random Binomial-Fibonacci sequences}},
  author = {Bernard Bercu and Fabrice Gamboa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37020},
  eprint = {2609.37020},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37020},
}
RIS
TY  - UNPB
TI  - On random Binomial-Fibonacci sequences
AU  - Bernard Bercu
AU  - Fabrice Gamboa
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37020
UR  - https://arxiv.org/abs/2609.37020
AB  - 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.
ER  -