[Forum SIS] Seminario BIRKNER

[Matteo Ruggiero]

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CICLO DI SEMINARI  -  COLLEGIO CARLO ALBERTO
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Nell'ambito del ciclo di seminari organizzato dalla
"de Castro" Statistics Initiative (www.carloalberto.org/stats),
alle ore 12.00 di Venerdi' 16 Marzo 2012,
presso la Sala Rossa del Collegio Carlo Alberto,
via Real Collegio 30, 10024, Moncalieri (TO),
si terra' il seguente seminario:

MATTHIAS BIRKNER (Johannes Gutenberg University Mainz, Germany)

ANCESTRAL LINEAGES UNDER LOCAL REGULATION

Abstract:
The spatial embeddings of genealogies in models with 
fluctuating population sizes and local regulation are relatively 
complicated random walks in a space-time dependent 
random environment. They seem presently not well understood. 
We use the supercritical discrete-time contact process on Z^d 
as the simplest non-trivial example of a locally regulated 
population model and study the dynamics of an ancestral 
lineage sampled at stationarity, viz. a directed random walk 
on a supercritical directed percolation cluster. We prove a 
law of large numbers and an annealed central limit theorem 
(CLT) for such a walk via a regenerative approach. Analysis 
of the joint dynamics of two walks in the same medium allows 
to obtain also a quenched CLT, at least in the case d≥3. 
Furthermore, we discuss approaches to extend these results 
to more general models that allow multiple occupancy of sites 
and implications for the spatial distribution of neutral types in 
equilibrium.
Based on joint work in progress with Jiri Cerny, Andrej 
Depperschmidt and Nina Gantert.


Tutti gli interessati sono invitati a partecipare.

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Matteo Ruggiero
University of Torino & Collegio Carlo Alberto
http://web.econ.unito.it/ruggiero

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