Hong Qian et al 1998 J. Phys. A: Math. Gen. 31 L527 doi:10.1088/0305-4470/31/28/002
On two-dimensional fractional Brownian motion and fractional Brownian random field
Hong Qian
,
, Gary M Raymond and James B Bassingthwaighte
LETTER TO THE EDITOR
As a generalization of one-dimensional fractional Brownian motion (1dfBm), we introduce a class of two-dimensional, self-similar, strongly correlated random walks whose variance scales with power law 
. We report analytical results on the statistical size and shape, and segment distribution of its trajectory in the limit of large N. The relevance of these results to polymer theory is discussed. We also study the basic properties of a second generalization of 1dfBm, the two-dimensional fractional Brownian random field (2dfBrf). It is shown that the product of two 1dfBms is the only 2dfBrf which satisfies the self-similarity defined by Sinai.
- PACS
- MSC
-
60J65 Brownian motion (See also 58J65)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
-
Issue 28 (17 July 1998)
Received 25 March 1998, in final form 1 June 1998
-
On two-dimensional fractional Brownian motion and fractional Brownian random field
Hong Qian et al 1998 J. Phys. A: Math. Gen. 31 L527
-
Multiple template-based fluoroscopic tracking of lung tumor mass without implanted fiducial markers
Ying Cui et al 2007 Phys. Med. Biol. 52 6229
-
Phase diagram of gauge glasses
Y Ozeki and H Nishimori 1993 J. Phys. A: Math. Gen. 26 3399
-
Subarcsecond Imaging of SiO in the HH 211 Protostellar Jet
Claire J. Chandler and John S. Richer 2001 ApJ 555 139
-
When is gttgrr = −1?
Ted Jacobson 2007 Class. Quantum Grav. 24 5717
-
Spinning test particles and clock effect in Kerr spacetime
Donato Bini et al 2004 Class. Quantum Grav. 21 5441
-
On representing observables in quantum mechanics
D A Dubin et al 2002 J. Phys. A: Math. Gen. 35 9113
-
Beyond Ehrenfest: correlated non-adiabatic molecular dynamics
Andrew P Horsfield et al 2004 J. Phys.: Condens. Matter 16 8251
-
Bosonic quadratic actions for 11-dimensional supergravity on AdS7/4 × S4/7
Fiorenzo Bastianelli and Roberto Zucchini 1999 Class. Quantum Grav. 16 3673
-
Integral equation and simulation studies of a planar nematogenic liquid in crossed external fields
F Lado et al 2005 J. Phys.: Condens. Matter 17 2801
Related review articles
What's this?- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain
- Universality of Wigner random matrices: a survey of recent results