scholarly journals A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpiński gasket

2017 ◽  
Vol 10 (2) ◽  
pp. 289-311 ◽  
Author(s):  
Kumiko Hattori ◽  
◽  
Noriaki Ogo ◽  
Takafumi Otsuka
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket ◽  
Self Avoiding Walk

On the recurrence of simple random walks on some fractals

1992 ◽  
Vol 29 (2) ◽  
pp. 454-459
Author(s):  
Zhou Xian-Yin
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Sierpinski Gasket ◽  
Simple Random Walk ◽  
Sierpinski Carpet ◽  
Sierpiński Gasket ◽  
Sierpiński Carpet

In this paper, the recurrence or transience of simple random walks on some lattice fractals is investigated. As results, we obtain that the simple random walk on the pre-Sierpinski gasket inddimensions is recurrent for alld≧ 2, and on the pre-Sierpinski carpet inddimensions it is recurrent ford= 2 and transient for alld≧ 3.

On the recurrence of simple random walks on some fractals

1992 ◽  
Vol 29 (02) ◽  
pp. 454-459
Author(s):  
Zhou Xian-Yin
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Sierpinski Gasket ◽  
Simple Random Walk ◽  
Sierpinski Carpet ◽  
Sierpiński Gasket ◽  
Sierpiński Carpet

In this paper, the recurrence or transience of simple random walks on some lattice fractals is investigated. As results, we obtain that the simple random walk on the pre-Sierpinski gasket in d dimensions is recurrent for all d ≧ 2, and on the pre-Sierpinski carpet in d dimensions it is recurrent for d = 2 and transient for all d ≧ 3.

Piecewise directed random walk on the Sierpinski gasket family of fractals

1989 ◽  
Vol 138 (9) ◽  
pp. 481-484 ◽  
Author(s):  
S. Elezović-Hadžić ◽  
S. Milošević
Keyword(s):  
Random Walk ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

EXACT FORMULA FOR THE MEAN LENGTH OF A RANDOM WALK ON THE SIERPINSKI TOWER

2002 ◽  
Vol 12 (11) ◽  
pp. 2379-2385 ◽  
Author(s):  
JOHN J. KOZAK ◽  
V. BALAKRISHNAN
Keyword(s):  
Random Walk ◽  
Arbitrary Number ◽  
Sierpinski Gasket ◽  
Exact Formula ◽  
Spectral Dimension ◽  
Sierpiński Gasket ◽  
Large N ◽  
The Mean

We consider an unbiased random walk on a finite, nth generation Sierpinski gasket (or "tower") in d = 3 Euclidean dimensions, in the presence of a trap at one vertex. The mean walk length (or mean number of time steps to absorption) is given by the exact formula [Formula: see text] The generalization of this formula to the case of a tower embedded in an arbitrary number d of Euclidean dimensions is also found, and is given by [Formula: see text] This also establishes the leading large-n behavior [Formula: see text] that may be expected on general grounds, where Nn is the number of sites on the nth generation tower and [Formula: see text] is the spectral dimension of the fractal.

scholarly journals Loop-erased random walk on the Sierpinski gasket

2014 ◽  
Vol 124 (1) ◽  
pp. 566-585 ◽  
Author(s):  
Kumiko Hattori ◽  
Michiaki Mizuno
Keyword(s):  
Random Walk ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

Random walks on the Sierpinski Gasket

1986 ◽  
Vol 47 (10) ◽  
pp. 1663-1669 ◽  
Author(s):  
R. Friedberg ◽  
O. Martin
Keyword(s):  
Random Walks ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket
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