Suggested Readings and Course Notes:

 

1/13/2005 - For the last lecture of Professor Shenker, please look at

 

http://www.physics.cornell.edu/sethna/teaching/562/HW/2003/pset07.pdf

 

and in particular sect. 7.5

 

More Reading on the Series by Shenker:

 

I.The Renormalization Group and the Wilson Fisher Fixed Point

 

Wilson, K. G. and Kogut, John , "The Renormalization group and the

epsilon expansion," Phys. Rept. 12,(1974) 75-200

 

Secs 1-4

 

II. Tunnelling in Quantum Mechanics from Path Integrals

(Instantons)

 

 "Aspects of Symmetry," Sidney Coleman, Cambridge University Press

(1985).

 

Chapter 7 Secs 1,2

 

Sketch the relation of this to the one dimensional Ising model at

low temperature.

 

 

 

III. The RG and  the One Dimensional Ising Model

 

"Soluble renormalization groups and scaling fields for

low-dimensional Ising systems"

 

DR Nelson and ME Fisher, Ann. Phys. 91 226-274 (1975)

 

 

 

IV. The RG in Chaos

 

M. J. Feigenbaum, "Quantitative universality for a class of

nonlinear transformations," J. Statist. Phys. 19 (1978), 25Ð52

 

 

V. The RG in nonlinear PDEs

 

"Anomalous dimensions and the renormalization group in a nonlinear

diffusion process,"

Nigel Goldenfeld, Olivier Martin, Y. Oono, and

Fong Liu, Phys. Rev. Lett. 64, 1361Ð1364 (1990).

 

VI.

 

Work through details of the RG approach to the Central Limit

Theorem discussed in class(see web link to Sethna).  Generalize to Levy

stable distributions and/or Poisson processes. See for example

http://www.applet-magic.com/mandel.htm

 

1/25/2005 - Some suggested reading for the first lecture of Persi Diaconis:

 

Shuffling Cards:

http://www.dartmouth.edu/~chance/teaching_aids/books_articles/Mann.pdf

Cutoff Phenomena:

http://www.pnas.org/cgi/reprint/93/4/1659.pdf

 

Stein's paradox:

(to come)

EFRON, B. and MORRIS, C. 1973 . Stein's estimation rule and its

competitors an empirical Bay es approach. J. Amer. Statist. Assoc. 68 117

130. Z . Mathematical Reviews: 52:9433

 

1/27/2005 - Lecture notes by Aharon Kapitulnik can be found HERE.

 

These notes include an introduction to disordered systems, introduction to critical phenomena and to percolation theory. They are also useful as a background for the lecture series by Steve Shenker.

 

For additional reading on Percolation theory look at:

 

  1. Dietrich Stauffer and Amnon Aharony, ÒIntroduction to percolation theoryÓ, 2nd ed. London: Taylor & Francis, 1992 (ISBN:0748400273).

 

  1. G. Grimmett: Percolation, 2nd ed., Springer, 1999. The Introduction is available on the web (A more math approach).

 

  1. D.J. Thouless in ÒIll Condensed Matter,Ó North Holland/World Scientific, 2nd ed. Singapore, 1983 (ISBN 9971-950-59-6).

 

  1. S. Kirkpatrick in ÒIll Condensed Matter,Ó North Holland/World Scientific, 2nd ed. Singapore, 1983 (ISBN 9971-950-59-6).

 

  1. Harry Kesten, The Annals of Probability 15, 1231 (1987) (Very math approach).

 

 

2/7/2005 - Lecture notes by Susan Holmes can be found HERE.

 

3/1/2005 - Here are some good links for updating Persi's lecture,

                            these are all good random number generator sites

 

 

ISAAC rng: http://burtleburtle.net/bob/rand/isaacafa.html

 

Mersenne Twister: http://www.math.keio.ac.jp/~matumoto/emt.html

 

Pierre L'Ecuyer's webpage: http://www.iro.umontreal.ca/~lecuyer/

 

Luc Devroye's webpage on random uniform and non uniform:

http://jeff.cs.mcgill.ca/~luc/rng.html

 

Numerical Recipe free online book chapter:

http://www.library.cornell.edu/nr/bookcpdf/c7-4.pdf

 

Random number generators available in R:

http://rweb.stat.umn.edu/R/library/base/html/Random.html

 

Uniform:Matlab resource:

http://www.csit.fsu.edu/~burkardt/m_src/uniform/uniform.html

 

Cryptographic Random Numbers: http://triumvir.org/rng/

 

MArsaglia's diehard tests and his random number generators:

http://www.cs.hku.hk/~diehard/cdrom/

 

 

3/4/2005 - More Lecture notes by Susan Holmes can be found HERE.

 

3/8/2005 Ð Relevant to SusanÕs last lecture:

 

Some useful links:

 

Projection Pursuit Notes on Indices and Examples:

 

http://www.stats.bris.ac.uk/~guy/Research/PP/PP.html

http://davis.wpi.edu/~matt/courses/nland/node4.html

http://www.quantlet.com/mdstat/scripts/mva/htmlbook/mvahtmlnode115.html

http://www.agocg.ac.uk/reports/visual/casestud/brunsdon/pursuit1.htm

 

Projection Pursuit Software:

 

http://sun.cwru.edu/~jiayang/nsf/ipp.html

http://www.ggobi.org/

http://www.research.att.com/areas/stat/xgobi/

 

Documentation:

 

http://www.public.iastate.edu/~dicook/ggobi-book/ggobi.html

 

How to get the wine data into R:

 

download.file(paste("ftp://ftp.ics.uci.edu/pub/",

                    "machine-learning-databases/wine/wine.data",

                    sep=''),

              "wine.data")

ds <- read.csv("wine.data", header = FALSE)

colnames(ds) <- c('Class', 'Alcohol', 'Malic', 'Ash',

                  'Alcalinity', 'Magnesium', 'Phenols',

                  'Flavanoids', 'Nonflavanoids',

                  'Proanthocyanins', 'Color', 'Hue',

                  'Dilution', 'Proline')

write.table(ds, "wine.csv", sep=",", row.names=FALSE)

 

Where is the WMAP data?

 

http://lambda.gsfc.nasa.gov/

 

 

What about the Quantum Field Theory and Bayesian Statistics link?

 

http://www.princeton.edu/~wbialek/our_papers/nemenman+bialek_02.pdf

http://astrosun.tn.cornell.edu/staff/loredo/bayes/fermi02.pdf

http://www.menem.com/~ilya/professional/talks/courant_102203.pdf

 

 

Bayesian Statistics Links are all at:

 

http://astrosun2.astro.cornell.edu/staff/loredo/bayes/