Category: Number Theory

Summary: Testing whether intermediate sign persistence in a Markov-modulated random Fibonacci recurrence creates the strongest finite-size intermittency while exponential growth still survives.

Random Fibonacci recurrences are a classic setting where simple rules generate subtle stochastic growth. This experiment asks what changes when the sign process is no longer independent from step to step, but instead has Markov persistence that creates runs of the same sign before switching.

The key question is whether moderate persistence produces a crossover regime with especially strong cancellation bursts and unusually large local-growth variance compared with both the independent-sign limit and the nearly deterministic limit. The simulation scans correlated two-state sign processes and summarizes the resulting finite-size intermittency while tracking whether long-run exponential growth remains intact.

That makes the project a correlation-structure test rather than another estimate for the iid case. The experiment targets a regime that sits between well-studied independent randomness and periodic or almost deterministic forcing.

Method: Repeated simulations of a random Fibonacci recurrence with a two-state Markov sign process, comparing intermittency statistics across persistence levels.

What is measured: Growth rate, local-growth variance, cancellation bursts, intermittency indicators, and dependence on sign persistence.