Topics in Probability Theory

FUTURE TALKS!!!!

Monday, February 14 10:15 S1

Erik Broman

Refinements of stochastic domination.
..............................................................
Tuesday February 22 13:15 S1. (DIFFERENT TIME THIS WEEK)

Frank den Hollander

Frank will give an informal seminar on some recent work entitled

Intermittency on catalyts

..............................................................
Monday, February 28 10:15 S1.

Serik Sagitov

Title: The coalescent with multiple mergers

Abstract: The coalescent is a continuous time Markov chain with finite number of states which builds
a random tree from leaves to the root. The basic coalescent with pairwise mergers is an important tool
of modern analysis of genetic variation within a population. This lecture reviews some recent papers
(1999-2004) by J. Schweinsberg, J.Pitman, M.Möhle, S.Sagitov, and R.Durrett introducing the coalescent
with multiple mergers and discussing its applications in population genetics.

PAST TALKS!!!!
...........................................................................
The first lecture is September 10.

Here are the coming lectures.

1. September 10.
Olle Haggstrom will be the first lecturer and he will
lecture on a new result related to first passage percolation. See
here, and here,

2. September 17, October 1,8 and 15.
Antar Bandyopadhyay will speak (a number of times) on his thesis
and follow up work (some with David Aldous) on recursive distributional equations
and its applications. The tentative plan is
1. Examples + General Set up, endogeny
2. Linear + Max-type RDEs, Applications : BRW
3. Applications : Trying to get rigorous argument for cavity method
or more on endogeny + Frozen percolation or hard-core model on random graphs.

Go here , for details on how to prepare for the above lectures.

3. October 22.
Daryl Daley:Australian National University, Canberra.
Title: Long range dependence of Markov chains in discrete time on countable state space

4. November 1 and November 15.
Johan Tykesson
Critical percolation on nonamenable graphs does not percolate.

5. November 22 and 29 and December 6.
Johan Jonasson
Various aspects of random walks on groups. Monday, January 24 10:15 S1.

Devdatt Dubhashi

Title: Progress on a classic of the Probabilistic method

Abstract: I will present an elegant proof that adorns the cover of the second edition of the book
"The Probabilistc Method" by N. Alon and J. Spencer. In a classic dating to the invention of the
"probabilistic method", Erdos showed in 1963 that any n-uniform hypergraph with lass than 2^{n-1}
edges can be 2-coloured so that no edge is monochromatic. He posed the extremal combinatorics
question: what is the least m = m(n) such that there is a n-uniform hypergraph with m edges
that is not 2-colourable? J. Radhakrishnan and A. Srnivasan showed in 2000 that
m(n) = \Omega(\sqrt{n/\log n} 2^n) with a gem that is short and elegant but nevertheless has
many hidden subtleties.
..............................................................
Monday, January 31 10:15 S1.

Jeff Steif

Title: Coin flipping protocols: an application of analysis to theoretical computer science.

Abstract: I will discuss a problem which comes from theoretic computer science but is essentially probability.
One of analytical tools needed for one of the problems is the "reverse Beckner inequality" (proved by
our own Christer Borell!). The usual Beckner (hypercontractivity) inequality has played an extremely
important role in theoretical computer science and I discussed this inequality in a stat/analysis seminar
a year ago. What I will talk about is the first application (as far as I know) of Borell's reverse Beckner
inequality to computer science.
(The work I describe is joint with E. Mossel, R. O'Donnell, O. Regev, and B. Sudakov.)