Random Fibonacci sequence: Difference between revisions

Revision as of 20:10, 5 May 2004

Revision as of 07:33, 25 June 2004

Line 22:

==Significance==

In 1960, [[Hillel Furstenberg]] and [[Harry Kesten]] had shown that for a general class of random [[matrix (math)|matrix]] products, the absolute value of the norm of product of ''n'' factors converges to a power of a fixed constant. This is a broad class of random sequence-generating processes, which includes the random Fibonacci sequence. This proof was significant in advances in [[laser]] technology and the study of [[glass]]es. The [[Nobel Prize for Physics]] in [[1977]] went to [[Philip Warren Anderson]] of [[Bell Laboratories]], [[Sir Nevill Francis Mott]] of [[Cambridge University]] in [[England]], and [[John Hasbrouck van Vleck ]] of [[Harvard]] "for their fundamental theoretical investigations of the electronic structure of magnetic and disordered systems".

Viswanath's proof, by specifying the value of the constant number in this case, has helped make this area more accessible for direct study. Viswanath's constant may explain the case of rabbits randomly allowed to prey on each other. (See [[Fibonacci sequence]] for the original statement of the rabbit problem.) This step would allow closer simulation of real world scenarios in various applications.