E Ben-Naim and P L Krapivsky 2006 J. Phys. A: Math. Gen. 39 L301 doi:10.1088/0305-4470/39/20/L02
Weak disorder in Fibonacci sequences
FREE ARTICLEE Ben-Naim1 and P L Krapivsky2
Show affiliationsLETTER TO THE EDITOR
We study how weak disorder affects the growth of the Fibonacci series. We introduce a family of stochastic sequences that grow by the normal Fibonacci recursion with probability 1 − 
, but follow a different recursion rule with a small probability . We focus on the weak disorder limit and obtain the Lyapunov exponent that characterizes the typical growth of the sequence elements, using perturbation theory. The limiting distribution for the ratio of consecutive sequence elements is obtained as well. A number of variations to the basic Fibonacci recursion including shift, doubling and copying are considered.
- PACS
-
02.30.Lt Sequences, series, and summability
02.10.De Algebraic structures and number theory
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
-
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
- Subjects
- Dates
-
Issue 20 (19 May 2006)
Received 6 March 2006
Published 3 May 2006
-
Weak disorder in Fibonacci sequences
E Ben-Naim and P L Krapivsky 2006 J. Phys. A: Math. Gen. 39 L301
-
HST/ACS Emission Line Imaging of Low-redshift 3CR Radio Galaxies. I. The Data
Grant R. Tremblay et al. 2009 ApJS 183 278
-
Scaling in tournaments
E. Ben-Naim et al 2007 EPL 77 30005
-
Addition–deletion networks
E Ben-Naim and P L Krapivsky 2007 J. Phys. A: Math. Theor. 40 8607
-
An experimental investigation on intra-fractional organ motion effects in lung IMRT treatments
Steve B Jiang et al 2003 Phys. Med. Biol. 48 1773
-
Scanning tunnelling microscopy and spectroscopy on organic PTCDA films deposited on sulfur passivated GaAs(001)
N Nicoara et al 2003 J. Phys.: Condens. Matter 15 S2619
-
Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm
Xiaoyan Ma et al 2003 Phys. Med. Biol. 48 4165
-
Neutrino flavour states and the quantum theory of neutrino oscillations
Carlo Giunti 2007 J. Phys. G: Nucl. Part. Phys. 34 R93
-
Nonlinear integral-equation formulation of orthogonal polynomials
Carl M Bender and E Ben-Naim 2007 J. Phys. A: Math. Theor. 40 F9
-
Exact helical reconstruction using native cone-beam geometries
Frédéric Noo et al 2003 Phys. Med. Biol. 48 3787
Users also read
What's this?Related review articles
What's this?- Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
- A property of the set of prime numbers
- Around the Davenport-Heilbronn function