Editing Random Fibonacci sequence (section)

{{Short description|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]] <math>f_n=f_{n-1}\pm f_{n-2}</math>, where the signs + or − are chosen [[Bernoulli distribution|at random]] with equal probability <math>\tfrac12</math>, [[Independence (probability theory)|independently]] for different <math>n</math>. By a [[theorem]] of [[Harry Kesten]] and [[Hillel Furstenberg]], random recurrent sequences of this kind grow at a certain [[exponential growth|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... {{OEIS|A078416}}, a [[mathematical constant]] that was later named Viswanath's constant.<ref>{{Cite journal | last1 = Viswanath | first1 = D. | title = Random Fibonacci sequences and the number 1.13198824... | doi = 10.1090/S0025-5718-99-01145-X | journal = Mathematics of Computation | volume = 69 | issue = 231 | pages = 1131–1155 | year = 1999 | doi-access = free }}</ref><ref>{{Cite journal | last1 = Oliveira | first1 = J. O. B. | last2 = De Figueiredo | first2 = L. H. | journal = Reliable Computing | volume = 8 | issue = 2 | pages = 131 |title=Interval Computation of Viswanath's Constant| year = 2002 | doi = 10.1023/A:1014702122205 | s2cid = 29600050 }}</ref><ref>{{Cite journal | last1 = Makover | first1 = E. | last2 = McGowan | first2 = J. | doi = 10.1016/j.jnt.2006.01.002 | title = An elementary proof that random Fibonacci sequences grow exponentially | journal = Journal of Number Theory | volume = 121 | pages = 40–44 | year = 2006 |arxiv=math.NT/0510159| s2cid = 119169165 }}</ref>