Lattice Random Walk in 2D

2007 ◽  
Keyword(s):  
Random Walk ◽  
Lattice Random Walk

Lattice random walk: an old problem with a future ahead

2018 ◽  
Vol 93 (9) ◽  
pp. 095201 ◽  
Author(s):  
Massimiliano Giona
Keyword(s):  
Random Walk ◽  
Lattice Random Walk

On the range of a constrained random walk

1988 ◽  
Vol 25 (03) ◽  
pp. 451-463
Author(s):  
W. Th. F. Den Hollander ◽  
G. H. Weiss
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Large Time ◽  
Statistical Properties ◽  
Time Limit ◽  
The Mean ◽  
Large Time Limit ◽  
Lattice Random Walk

We study statistical properties of the range (= number of distinct sites visited) of a lattice random walk in discrete time constrained to visit a given site at a given time. In particular, we calculate the mean and obtain a bound on the variance of the range in the large time limit. The results are applied to a problem involving an unconstrained random walk in the presence of randomly distributed traps. A key role is played by the associated random walk that is obtained from the original random walk via a Cramer transform.

On the range of a constrained random walk

1988 ◽  
Vol 25 (3) ◽  
pp. 451-463 ◽  
Author(s):  
W. Th. F. Den Hollander ◽  
G. H. Weiss
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Large Time ◽  
Statistical Properties ◽  
Time Limit ◽  
The Mean ◽  
Large Time Limit ◽  
Lattice Random Walk

We study statistical properties of the range (= number of distinct sites visited) of a lattice random walk in discrete time constrained to visit a given site at a given time. In particular, we calculate the mean and obtain a bound on the variance of the range in the large time limit. The results are applied to a problem involving an unconstrained random walk in the presence of randomly distributed traps. A key role is played by the associated random walk that is obtained from the original random walk via a Cramer transform.

A correlated random walk model for two-dimensional diffusion

1984 ◽  
Vol 21 (2) ◽  
pp. 233-246 ◽  
Author(s):  
Robin Henderson ◽  
Eric Renshaw ◽  
David Ford
Keyword(s):  
Random Walk ◽  
Transition Probabilities ◽  
Exact Expression ◽  
Dispersion Matrix ◽  
Two Dimensional ◽  
Correlated Random Walk ◽  
Dimensional Diffusion ◽  
Step Transition ◽  
Lattice Random Walk ◽  
Previous Step

A two-dimensional lattice random walk is studied in which, at each stage, the direction of the next step is correlated to that of the previous step. An exact expression is obtained from the characteristic function for the dispersion matrix of the n-step transition probabilities, and the limiting diffusion equation is derived.

A correlated random walk model for two-dimensional diffusion

1984 ◽  
Vol 21 (02) ◽  
pp. 233-246 ◽  
Author(s):  
Robin Henderson ◽  
Eric Renshaw ◽  
David Ford
Keyword(s):  
Random Walk ◽  
Transition Probabilities ◽  
Exact Expression ◽  
Dispersion Matrix ◽  
Two Dimensional ◽  
Correlated Random Walk ◽  
Dimensional Diffusion ◽  
Step Transition ◽  
Lattice Random Walk ◽  
Previous Step

A two-dimensional lattice random walk is studied in which, at each stage, the direction of the next step is correlated to that of the previous step. An exact expression is obtained from the characteristic function for the dispersion matrix of the n-step transition probabilities, and the limiting diffusion equation is derived.

Sign in / Sign up

Export Citation Format

Share Document