Percolation of coalescing random walks

1990 ◽  
Vol 27 (2) ◽  
pp. 269-277 ◽  
Author(s):  
Bao Gia Nguyen
Keyword(s):  
Random Walks ◽  
Binary Tree ◽  
Longest Path ◽  
Image Position ◽  
Coalescing Random Walks

We study the shape of the binary tree containing 0 that is created from percolation of coalescing random walks. The key result is a duality lemma describing the shape of the tree. Furthermore, we show that and where A(R0), M(R0), L(R0) are respectively the area, the number of external nodes and the length of the longest path of the tree R0.

Percolation of coalescing random walks

1990 ◽  
Vol 27 (02) ◽  
pp. 269-277 ◽  
Author(s):  
Bao Gia Nguyen
Keyword(s):  
Random Walks ◽  
Binary Tree ◽  
Longest Path ◽  
Image Position ◽  
Coalescing Random Walks

We study the shape of the binary tree containing 0 that is created from percolation of coalescing random walks. The key result is a duality lemma describing the shape of the tree. Furthermore, we show that and where A(R 0), M(R 0), L(R 0) are respectively the area, the number of external nodes and the length of the longest path of the tree R 0.

Discounted branching random walks

1985 ◽  
Vol 17 (01) ◽  
pp. 53-66
Author(s):  
K. B. Athreya
Keyword(s):  
Functional Equation ◽  
Random Walks ◽  
Unique Solution ◽  
Log P ◽  
Branching Random Walks ◽  
Probabilistic Construction ◽  
Image Position

Let F(·) be a c.d.f. on [0,∞), f(s) = ∑∞ 0 pjsi a p.g.f. with p 0 = 0, < 1 < m = Σj p j < ∞ and 1 < ρ <∞. For the functional equation for a c.d.f. H(·) on [0,∞] we establish that if 1 – F(x) = O(x –θ ) for some θ > α =(log m)/(log p) there exists a unique solution H(·) to (∗) in the class C of c.d.f.’s satisfying 1 – H(x) = o(x –α ). We give a probabilistic construction of this solution via branching random walks with discounting. We also show non-uniqueness if the condition 1 – H(x) = o(x –α ) is relaxed.

scholarly journals Large void zones and occupation times for coalescing random walks

2004 ◽  
Vol 111 (1) ◽  
pp. 97-118
Author(s):  
Endre Csáki ◽  
Pál Révész ◽  
Zhan Shi
Keyword(s):  
Random Walks ◽  
Occupation Times ◽  
Large Void ◽  
Coalescing Random Walks

scholarly journals Coalescing Random Walks and Voting on Connected Graphs

2013 ◽  
Vol 27 (4) ◽  
pp. 1748-1758 ◽  
Author(s):  
Colin Cooper ◽  
Robert Elsässer ◽  
Hirotaka Ono ◽  
Tomasz Radzik
Keyword(s):  
Random Walks ◽  
Connected Graphs ◽  
Coalescing Random Walks

scholarly journals Mean field conditions for coalescing random walks

2013 ◽  
Vol 41 (5) ◽  
pp. 3420-3461 ◽  
Author(s):  
Roberto Imbuzeiro Oliveira
Keyword(s):  
Random Walks ◽  
Mean Field ◽  
Field Conditions ◽  
Coalescing Random Walks

Discounted branching random walks

1985 ◽  
Vol 17 (1) ◽  
pp. 53-66 ◽  
Author(s):  
K. B. Athreya
Keyword(s):  
Functional Equation ◽  
Random Walks ◽  
Unique Solution ◽  
Log P ◽  
Branching Random Walks ◽  
Probabilistic Construction ◽  
Image Position

Let F(·) be a c.d.f. on [0,∞), f(s) = ∑∞0pjsi a p.g.f. with p0 = 0, < 1 < m = Σjpj < ∞ and 1 < ρ <∞. For the functional equation for a c.d.f. H(·) on [0,∞] we establish that if 1 – F(x) = O(x–θ) for some θ > α =(log m)/(log p) there exists a unique solution H(·) to (∗) in the class C of c.d.f.’s satisfying 1 – H(x) = o(x–α).We give a probabilistic construction of this solution via branching random walks with discounting. We also show non-uniqueness if the condition 1 – H(x) = o(x–α) is relaxed.

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