Catalytic Branching Random Walk on a Two-Dimensional Lattice

2011 ◽  
Vol 55 (1) ◽  
pp. 120-126 ◽  
Author(s):  
E. Vl. Bulinskaya
Keyword(s):  
Random Walk ◽  
Branching Random Walk ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Catalytic Branching

Maximum of a catalytic branching random walk

2019 ◽  
Vol 74 (3) ◽  
pp. 546-548 ◽  
Author(s):  
E. Vl. Bulinskaya
Keyword(s):  
Random Walk ◽  
Branching Random Walk ◽  
Catalytic Branching

Random walk and SU(2) Clebsch–Gordon coefficients

1979 ◽  
Vol 57 (11) ◽  
pp. 2050-2051
Author(s):  
F. Lemire ◽  
J. Patera
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Transition Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
New Interpretation ◽  
Source Of Information

This article contains a new interpretation of the values of the SU(2) Clebsch–Gordon coefficients (CGC). It is shown that a given CGC C(l1,l2,l;m1,m2,m) can be understood as a transition function for a random walk on a two dimensional lattice between the origin and the point (m1,m2) in l1 + l2 + l steps. This interpretation is based on the generating function for the CGC which has previously been shown to be a rich and concise source of information on the CGC.

scholarly journals Individuals at the origin in the critical catalytic branching random walk

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Valentin Topchii ◽  
Vladimir Vatutin
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Continuous Time ◽  
Branching Random Walk ◽  
Conditional Limit Theorem ◽  
Catalytic Branching ◽  
International Audience ◽  
Number Of Individuals ◽  
Conditional Limit

International audience A continuous time branching random walk on the lattice $\mathbb{Z}$ is considered in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we prove a conditional limit theorem for the number of individuals at the origin.

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