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Seminar Announcement**

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*Coalescence in branching processes*


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*Krishna Athreya*

***Department of Statistics*

*Iowa State University*

*_Johnson Center G19 - Gold Room _*

*_4400 University Drive, Fairfax, VA 22030_*__

*_Time: 11:00 A.M. - 12:00 P.M._*__

*_Date: Friday, Sep 14, 2012 _*__

*Abstract*

Consider a branching tree. Go to the nth generation. If there are at 
least two vertices in that generation pick two of them at random by 
srswor (simple random sampling without replacement) and trace their 
lines of descent back in time till they meet. Call that generaion Xn. Do 
the same thing with all individuals in the nth generation. Call that Yn. 
In this talk we discuss the distributions of Xn and Yn and their 
asymptotics for Galton Watson trees as n goes to infinity for single and 
multitype cases for the four cases: subcritical, critical, 
supercritical, explosive.Applications to branching random walks will 
also be discussed.



-- 
Yunpeng Zhao, PhD

Assistant Professor
Department of Statistics
Volgenau School of Engineering<mailto:[log in to unmask]>
George Mason University
Engineering Building, Room 1719, MS 4A7
4400 University Drive
Fairfax, VA 22030-4444

Phone: 703-993-1674
Email: [log in to unmask] <mailto:[log in to unmask]>