Technion, IEM faculty - Seminar in Probability and Stochastic Processes
Speaker: Anita Winter

Title: Coalescent processes arising in a study of diffusive clustering

Date: 29/03/2011

Time: 11:30

Place: Hashmal-861

Abstract:  <http://ie.technion.ac.il/seminar_files/1300112137_W.txt>

Or just read it on the following lines:

In this talk we consider the spatially structured coalescent on $\Z^2$.
The system starts either in locally finite configurations or in
configurations containing countably many partition elements  per site.

We determine the longtime behavior with an initial population restricted to the box
$\Lambda^{\alpha,t}:=[-t^{\alpha/2}, t^{\alpha/2}]^2 \cap \Z^2$
and observed at time $t^\beta$ where $1 \geq \beta \geq \alpha\ge 0$.
We study both longterm asymptotics
for a fixed value of $\alpha$
as the parameter $\beta\in[\alpha,1]$ varies
as well for a fixed $\beta$,
as the parameter $\alpha\in [0,\beta]$ varies.

A new random object, the so-called coalescent with rebirth,
is constructed via a look-down procedure. It arises in the longterm space-time
limit of the coalescent restricted to $\Lambda^{\alpha,t}$ with $\alpha\in[0,1]$
and observed at time $t$.

(joint work with Andreas Greven and Vlada Limic)

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