Asymptotic properties of multistate random walks. II. Applications to inhomogeneous periodic and random lattices

1985 ◽  
Vol 41 (3-4) ◽  
pp. 581-606 ◽  
Author(s):  
J. B. T. M. Roerdink ◽  
K. E. Shuler
Keyword(s):  
Random Walks ◽  
Asymptotic Properties ◽  
Random Lattices ◽  
Multistate Random Walks

A note on the asymptotic properties of correlated random walks

1985 ◽  
Vol 22 (4) ◽  
pp. 951-956 ◽  
Author(s):  
J. B. T. M. Roerdink
Keyword(s):  
Asymptotic Behavior ◽  
Random Walks ◽  
Asymptotic Properties ◽  
Simple Relation ◽  
Finite Variance ◽  
Correlated Random Walk ◽  
Expected Number ◽  
Similar Relation ◽  
Correlated Random Walks ◽  
Multistate Random Walks

We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.

Exact and asymptotic properties of multistate random walks

1991 ◽  
Vol 65 (1-2) ◽  
pp. 167-182 ◽  
Author(s):  
Carlos B. Briozzo ◽  
Carlos E. Budde ◽  
Omar Osenda ◽  
Manuel O. C�ceres
Keyword(s):  
Random Walks ◽  
Asymptotic Properties ◽  
Multistate Random Walks

Asymptotic properties of multistate random walks. I. Theory

1985 ◽  
Vol 40 (1-2) ◽  
pp. 205-240 ◽  
Author(s):  
J. B. T. M. Roerdink ◽  
K. E. Shuler
Keyword(s):  
Random Walks ◽  
Asymptotic Properties ◽  
Multistate Random Walks

A note on the asymptotic properties of correlated random walks

1985 ◽  
Vol 22 (04) ◽  
pp. 951-956 ◽  
Author(s):  
J. B. T. M. Roerdink
Keyword(s):  
Asymptotic Behavior ◽  
Random Walks ◽  
Asymptotic Properties ◽  
Simple Relation ◽  
Finite Variance ◽  
Correlated Random Walk ◽  
Expected Number ◽  
Similar Relation ◽  
Correlated Random Walks ◽  
Multistate Random Walks

We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.

Random walks on random lattices with traps

1983 ◽  
Vol 30 (2) ◽  
pp. 373-381 ◽  
Author(s):  
V. Halpern
Keyword(s):  
Random Walks ◽  
Random Lattices

scholarly journals On the csáki-vincze transformation

2013 ◽  
Vol 50 (2) ◽  
pp. 266-279
Author(s):  
Hatem Hajri
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Asymptotic Properties ◽  
Scaling Limit ◽  
Simple Random Walk ◽  
Precise Description ◽  
Discrete Transformation

Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T. We prove that T is exact: ∩k≧1σ(Tk(S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scaling limit, all iterations of T “converge” to the corresponding iterations of the continuous Lévy transform of Brownian motion.

Sign in / Sign up

Export Citation Format

Share Document