[Ml-stat-talks] SAS Spring 2013: Random graphs

Ramon van Handel rvan at Princeton.EDU
Fri Feb 15 15:14:53 EST 2013


Dear all,

This semester, we aim to resume the informal seminar part of the Stochastic 
Analysis Seminar as in the last couple of semesters.  We are on a shortened 
eight-week schedule, however, due to an exceptionally busy February.

This spring, we will attempt an introduction to random graphs, or, to be more 
precise, Erdos-Renyi random graphs.  We are aiming only for some of the most 
basic results that can be covered in detail in eight weeks.  The abstract is 
attached at the bottom of this email.

Your friendly lecturers this semester may include Sebastien Bubeck, Rene 
Carmona, Philippe Rigollet and yours truly. The lectures will be held on 
Thursdays from 4:30-6:00 starting February 28, 2013 in Bendheim Center 
classroom 103. Further details/updates will be posted at 
http://orfe.princeton.edu/sas .

As always, all are welcome. Looking forward to seeing you at the seminar!

    -- Ramon

PS: there will be no regular outside stochastic analysis seminar speakers this 
semester. Outside speakers will resume at some point in the future.


Spring 2013: Random graphs

Complex graphs and networks are ubiquitous throughout science and engineering, 
and possess beautiful mathematical properties.  The goal of these informal 
lectures is to provide an introduction to some of the most basic results in the 
theory of (Erdos-Renyi) random graphs from the probabilistic viewpoint: 
chromatic number and clique number, and the size of the largest component in 
the subcritical, supercritical, and critical regimes.  If time permits, we will 
discuss Brownian limits.

Prerequisites: Probability at the level of ORF 526 is assumed.

Time and location: Thursdays, 4:30-6:00, Bendheim Center classroom 103.
The first lecture will be on February 28.
There will be no lecture on March 28.

References:

* Alon and Spencer, "The Probabilistic Method", Wiley.

* Durrett, "Random Graph Dynamics", Cambridge.

* Nachmias and Peres, "The critical random graph, with martingales", Israel J. 
Math. 176 (2010), p. 29-41.

* Aldous, "Brownian excursions, critical random graphs and the multiplicative 
coalescent", Ann. Probab. 25 (1997), p. 812-854.

* van der Hofstad, "Random Graphs and Complex Networks", lecture notes,
http://www.win.tue.nl/~rhofstad/NotesRGCN.pdf

* Bollobas, "Random Graphs", Cambridge.

* Janson, Luczak, Rucinski, "Random Graphs", Wiley.



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