Probability Study Group

This is an informal study group covering topics in probability. Speakers volunteer to present recent papers on topics selected by the group at large. Grad students, postdocs, and faculty are all encouraged to attend.

Details

A model of migration under constraints

by Raoul Normand | Paris 6 and Toronto
Time: 14:10  (Friday, Dec. 02, 2011)
Location: BA6180, Bahen Center, 40 St. George St.
Abstract:
The goal of this talk is to present a simple model of population with migration. The tools used are classical, namely Galton-Watson trees, random walks and Brownian motion, so this talk is accessible to graduate students. In our model, migrations are constrained, in that people migrate when the resources on the "island" where they live are exhausted. From the genealogy of an individual (a Galton-Watson tree), we can construct the "tree of isles", describing the genealogy of the migrations. A first step is to describe this tree. The second step is to study limits. The relevant parameters are encoded in a random walk, and thus the limiting quantities are related to the Brownian motion.

Dates in this series

· Monday, Feb. 08, 2010: Liouville Property, Amenability, Discrete Fractals and Automaton Groups (Gidi Amir)
· Monday, Feb. 22, 2010: Scaling Exponents for Directed Polymers in 1+1 Dimensions, Part III (Tom Alberts)
· Monday, Mar. 01, 2010: Scaling exponents for directed polymers in dimension 1+1, part III (Tom Alberts)
· Monday, Apr. 26, 2010: More details of Jeff Schenker's proof of eigenvector localization for band matrices (Ben Rifkind)
· Monday, May. 10, 2010: The Doob h-transform: theory and examples (Alex Bloemendal)
· Monday, May. 17, 2010: Doob's h-transform: a few more examples (Alex Bloemendal)
· Monday, Oct. 04, 2010: Sample Path Properties of Stochastic Flows (Dima Dolgopyat)
· Monday, Oct. 18, 2010: Sample Path Properties of Stochastic Flows, Part II (Dima Dolgopyat)
· Monday, Oct. 25, 2010: Sample Path Properties of Stochastic Flows, Part III (Dima Dolgopyat)
· Friday, Jul. 29, 2011: SLE in multiply connected domains (Gregory F. Lawler)
· Friday, Dec. 02, 2011: A model of migration under constraints (Raoul Normand)
· Friday, Jan. 20, 2012: Local Limit Theorem for Random Walks on Free Groups (Andrew Stewart)
· Friday, Feb. 03, 2012: The Law of the Iterated Logarithm (Eric Hart)
· Friday, Mar. 16, 2012: Random matrices: Getting inside the bulk! (Van Vu)
· Friday, Mar. 30, 2012: A Brief Introduction to Compressed Sensing (Kai Yang)
· Friday, Apr. 13, 2012: The Minimum Cost of a Random Assignment (Mustazee Rahman)
· Tuesday, May. 01, 2012: An Introduction to the Dirichlet Process (Tom Alberts)