Randomized mathematical sequence based upon the Fibonacci sequence
In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation , where the signs + or − are chosen at random with equal probability , independently for different . By a theorem of Harry Kesten and Hillel Furstenberg, random recurrent sequences of this kind grow at a certain exponential rate, but it is difficult to compute the rate explicitly. In 1999, Divakar Viswanath showed that the growth rate of the random Fibonacci sequence is equal to 1.1319882487943... (sequence A078416 in the OEIS), a mathematical constant that was later named Viswanath's constant.[1][2][3]
^Viswanath, D. (1999). "Random Fibonacci sequences and the number 1.13198824..." Mathematics of Computation. 69 (231): 1131–1155. doi:10.1090/S0025-5718-99-01145-X.
^Oliveira, J. O. B.; De Figueiredo, L. H. (2002). "Interval Computation of Viswanath's Constant". Reliable Computing. 8 (2): 131. doi:10.1023/A:1014702122205. S2CID 29600050.
^Makover, E.; McGowan, J. (2006). "An elementary proof that random Fibonacci sequences grow exponentially". Journal of Number Theory. 121: 40–44. arXiv:math.NT/0510159. doi:10.1016/j.jnt.2006.01.002. S2CID 119169165.
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