Breakdown of Alexander-Orbach conjecture for percolation: Exact enumeration of random walks on percolation backbones

1984 ◽  
Vol 30 (7) ◽  
pp. 4083-4086 ◽  
Author(s):  
Daniel C. Hong ◽  
Shlomo Havlin ◽  
Hans J. Herrmann ◽  
H. Eugene Stanley
Keyword(s):  
Random Walks ◽  
Exact Enumeration

Exact-enumeration approach to random walks on percolation clusters in two dimensions

1984 ◽  
Vol 30 (3) ◽  
pp. 1626-1628 ◽  
Author(s):  
Imtiaz Majid ◽  
Daniel Ben- Avraham ◽  
Shlomo Havlin ◽  
H. Eugene Stanley
Keyword(s):  
Random Walks ◽  
Two Dimensions ◽  
Exact Enumeration ◽  
Percolation Clusters

Exact enumeration of random walks with traps

1984 ◽  
Vol 17 (6) ◽  
pp. L347-L350 ◽  
Author(s):  
S Havlin ◽  
G H Weiss ◽  
J E Kiefer ◽  
M Dishon
Keyword(s):  
Random Walks ◽  
Exact Enumeration

On random walks with restricted reversals

1958 ◽  
Vol 54 (1) ◽  
pp. 48-59 ◽  
Author(s):  
C. Domb ◽  
M. E. Fisher
Keyword(s):  
Random Walks ◽  
Distribution Functions ◽  
Asymptotic Estimates ◽  
Exact Enumeration ◽  
Chain Molecules ◽  
Physical Interest ◽  
Cooperative Phenomena ◽  
Starting Point ◽  
Correlated Random Walks ◽  
Long Chain

1. Introduction. Problems of unrestricted random walks on lattices have been considered by many authors and methods have been discovered for the exact enumeration of the number of walks between two points, for obtaining asymptotic estimates of the distribution functions and for evaluating special parameters such as the probability of ultimate retum to the starting point. By an unrestricted walk we mean one in which the probability of the next step at any stage is not influenced by the previous choice of steps. The corresponding problems for restricted (or correlated) random walks are more difficult and fewer results have been obtained. Restricted walks are, however, of considerable physical interest in connexion with the statistical behaviour of long chain molecules, the theory of cooperative phenomena in crystals and in other applications.

scholarly journals Exact enumeration approach to first-passage time distribution of non-Markov random walks

2019 ◽  
Vol 99 (6) ◽  
Author(s):  
Shant Baghram ◽  
Farnik Nikakhtar ◽  
M. Reza Rahimi Tabar ◽  
S. Rahvar ◽  
Ravi K. Sheth ◽  
...  
Keyword(s):  
Random Walks ◽  
Time Distribution ◽  
First Passage Time ◽  
Passage Time ◽  
Exact Enumeration ◽  
First Passage ◽  
Markov Random

RESTRICTED RANDOM WALK NUMBERS OF THE FIRST AND SECOND KIND

2004 ◽  
Vol 03 (02) ◽  
pp. 155-162 ◽  
Author(s):  
A. S. PADMANABHAN
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Stirling Numbers ◽  
Exact Enumeration ◽  
Finite Memory ◽  
Definition Of

In a manner analogous to the definition of Stirling numbers of the first and second kind we define a set of numbers for restricted random walks of finite memory. These two sequences of counting numbers should be useful in the exact enumeration of properties of simple and restricted random walks.

AN EFFICIENT IMPLEMENTATION OF THE EXACT ENUMERATION METHOD FOR RANDOM WALKS ON SIERPINSKI CARPETS

Fractals ◽  
2000 ◽  
Vol 08 (02) ◽  
pp. 155-161 ◽  
Author(s):  
ASTRID FRANZ ◽  
CHRISTIAN SCHULZKY ◽  
STEFFEN SEEGER ◽  
KARL HEINZ HOFFMANN
Keyword(s):  
Probability Distribution ◽  
Random Walks ◽  
Mean Square Displacement ◽  
Computation Time ◽  
Scaling Exponent ◽  
Exact Enumeration ◽  
Time Step ◽  
The Mean ◽  
Dynamic Data Structure ◽  
Sierpinski Carpets

In the following, we present a highly efficient algorithm to iterate the master equation for random walks on effectively infinite Sierpinski carpets, i.e. without surface effects. The resulting probability distribution can, for instance, be used to get an estimate for the random walk dimension, which is determined by the scaling exponent of the mean square displacement versus time. The advantage of this algorithm is a dynamic data structure for storing the fractal. It covers only a little bit more than the points of the fractal with positive probability and is enlarged when needed. Thus the size of the considered part of the Sierpinski carpet need not be fixed at the beginning of the algorithm. It is restricted only by the amount of available computer RAM. Furthermore, all the information which is needed in every step to update the probability distribution is stored in tables. The lookup of this information is much faster compared to a repeated calculation. Hence, every time step is speeded up and the total computation time for a given number of time steps is decreased.

Non-homogeneous Random Walks

2016 ◽  
Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Andrew Wade
Keyword(s):  
Random Walks
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