Annihilating and coalescing random walks on ? d

1978 ◽  
Vol 46 (1) ◽  
pp. 55-65 ◽  
Author(s):  
David Griffeath
Keyword(s):  
Random Walks ◽  
Coalescing Random Walks

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

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.

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

scholarly journals Spatially Inhomogeneous Populations with Seed-Banks: I. Duality, Existence and Clustering

2021 ◽  
Author(s):  
Frank den Hollander ◽  
Shubhamoy Nandan
Keyword(s):  
Random Walks ◽  
Seed Bank ◽  
Seed Banks ◽  
Model Parameters ◽  
Geographic Space ◽  
Spatially Inhomogeneous ◽  
And Migration ◽  
Coalescing Random Walks ◽  
Colony Migration

AbstractWe consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. The colonies are labelled by $${\mathbb {Z}}^d$$ Z d , $$d \ge 1$$ d ≥ 1 , playing the role of a geographic space. The sizes of the active and the dormant population are finite and depend on the location of the colony. Migration is driven by a random walk transition kernel. Our goal is to study the equilibrium behaviour of the system as a function of the underlying model parameters. In the present paper, under a mild condition on the sizes of the active populations, the system is well defined and has a dual. The dual consists of a system of interacting coalescing random walks in an inhomogeneous environment that switch between an active state and a dormant state. We analyse the dichotomy of coexistence (= multi-type equilibria) versus clustering (= mono-type equilibria) and show that clustering occurs if and only if two random walks in the dual starting from arbitrary states eventually coalesce with probability one. The presence of the seed-bank enhances genetic diversity. In the dual this is reflected by the presence of time lapses during which the random walks are dormant and do not move.

scholarly journals From Coalescing Random Walks on a Torus to Kingman’s Coalescent

2019 ◽  
Vol 177 (6) ◽  
pp. 1172-1206
Author(s):  
J. Beltrán ◽  
E. Chavez ◽  
C. Landim
Keyword(s):  
Random Walks ◽  
Coalescing Random Walks ◽  
Kingman’S Coalescent

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.

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