Here is a suggestion list for what one might want to look at before my
three talks in the graduate seminar course.
These are all from the
survey paper with Prof. Aldous which is available from the arXiv link
here . Few other
references are also included.
Talk-1 :
* Examples : Chapter 1 : Look at the "Table-1".
Skip section 1.1 and 1.2 for first reading.
* General Setup and Endogeny : Chapter-2 : Skip "Figure-2" and Section 2.6
for the first reading.
Also look at Chapter 9 (half a page) to get a general feeling of what we
are trying to do here.
Talk-2 :
* Bivariate uniqueness : Chapter-2 : Section 2.4
* Equivalence Theorem : Chapter-2 : Section 2.5
* Frozen Percolation process : Chapter-6 : Existence on binary tree;
non-existence on Z^2-lattice;
proof of endogeny.
Talk-3 :
* Linear RDE : Chapter 3 : Theorem 16 and discussion, Section 3.2.
Skip Section 3.1 for the first reading.
* Max-type RDEs : Chapter 4 : Sections 4.1, 4.2, 4.4 (and may be 4.5)
[just statements of the results]
Skip Sections 4.3 and 4.6 for first reading.
* BRW : Chapter 5 : Sections 5.1, 5.2, 5.3 (for 5.3 just looks at the Open
Problem 46 and statement of the Proposition 48).
* Limit of BRW : "Back to linear" method (not written yet !)
References :
[1] D. J. Aldous and A. Bandyopadhyay. A Survey of Max-Type Recursive Distributional Equations. To appear at Ann. Appl. Probab.,
available at
http://www.arxiv.org/pdf/math.PR/0401388, 2004.
[2] D. J. Aldous. The percolation process on a tree where infinite clusters are frozen. Math. Proc. Cambridge Philos. Soc., 128:465-477, 2000.
[3] A. Bandyopadhyay. Bivariate Uniqueness and Endogeny for Recursive Distributional Equations : Two Examples. available at
http://www.arxiv.org/pdf/math.PR/0407175, 2004.