CS294 Markov Chain Monte Carlo: Project Suggestions
Below is a list of suggestions for project topics. Please read the
detailed guidelines here first.
Once you have made your selections, please email me your first choice
plus at least one, and preferably two, alternatives.
Projects marked XXX have already been selected by someone.
Deadline for selecting a project: Friday November 6!

Detailed analysis of card shuffles. [Bayer & Diaconis,
Annals of Applied Probability, 1992; Diaconis, Fill & Pitman,
Combinatorics, Probability & Computing, 1992.]

XXX The Kruskal Count and Wild Kangaroos. [Lagarias, Rains and Vanderbei, 2009;
Montenegro and Tetali, ACM STOC, 2009.]

More on strong stationary times. [Aldous & Diaconis,
Advances in Applied Math., 1987; Diaconis & Fill,
Annals of Probability, 1990.]

More on stopping rules. [Lovasz & Winkler, London Math. Soc.
Lecture Note Series 218, 1995, and references therein.]

XXX Group representations and mixing times. [Diaconis & Shashahani,
Zeitschrift fuer Wahrscheinlichkeitstheorie, 1981;
Diaconis, Group Representations in Probability & Statistics,
1988.]

XXX Generating a Random Spanning Tree. [Aldous, SIAM Journal of Discrete
Math, 1990; Broder, IEEE FOCS, 1989; Wilson, ACM STOC, 1996.]

More on coupling for colorings.
[Dyer/Frieze, Random Structures & Algorithms, 2003; Hayes/Vigoda,
ACMSIAM SODA, 2005.]

Tight analysis of the lozenge tilings Markov chain. [Wilson, Annals of
Applied Probability, 2004.]

More on Coupling from the Past  An interruptible algorithm. [Fill,
Annals of Applied Prob., 1998; Fill, Machida, Murdoch & Rosenthal,
Random Structures & Algorithms, 2000.]

Impossibility of finding an efficient Markovian coupling for Markov chains on matchings.
[Kumar & Ramesh, IEEE FOCS, 1999.]

Polynomial time algorithms for the Ising model. [Jerrum & Sinclair, SIAM Journal on
Computing, 1993.]

XXX Truncated cubes and the knapsack problem. [Morris & Sinclair,
SIAM Journal on Computing, 2004.]

The mixing time of the Thorp shuffle. [Morris, ACM STOC, 2004;
Morris Annals of Probability, to appear (see http://front.math.ucdavis.edu/0802.0339).]

An alternative bound on mixing times: Evolving Sets. [Morris & Peres,
ACM STOC, 2003; full version in Probability Theory & Related Fields, 2005.]

XXX Application of Evolving Sets to clustering. [Anderson & Peres,
ACM STOC, 2009.]

Another alternative bound on mixing times: the logSobolev inequality. [Diaconis
& SaloffCoste, Annals of Applied Prob., 1996; Frieze & Kannan,
Annals of Applied Prob., 1999.]

Yet another alternative bound: Nash inequalities. [Diaconis
& SaloffCoste, Journal of Theoretical Probability, 1996.]

XXX State of the art on volume computation. [Lovasz & Vempala, IEEE FOCS,
2003.]

Sampling problems associated with matroids. [Feder & Mihail, ACM
STOC, 1992; Azar, Broder & Frieze, Information Processing
Letters, 1994; Jerrum & Son, IEEE FOCS, 2002.]

Negative results on simulated annealing for maximum matching. [Sasaki
& Hajek, Journal of the ACM, 1988.]

Simulated tempering: a twist on simulated annealing. [Geyer
& Thompson, Journal of the American Statistical Association,
1995; Madras & Piccioni, Annals of Applied Probability, 1999.]

XXX The Dobrushin uniqueness condition: a "rapid mixing'' condition from
statistical physics. [Weitz, Random Structures & Algorithms, 2005;
Hayes, IEEE FOCS, 2006.]
 Slow mixing in Markov chains. [Gore & Jerrum, ACM STOC, 1997;
Borgs et al., IEEE FOCS, 1999.]
 A lower bound for Glauber dynamics. [Hayes & Sinclair, IEEE FOCS, 2005.]

The Ising model on trees. [Kenyon, Mossel and Peres, IEEE FOCS, 2001;
Martinelli, Sinclair and Weitz, IEEE FOCS, 2003.]

XXX Computing the surface area of a convex body. [Belkin, Narayanan & Niyogi,
IEEE FOCS, 2006.]

XXX An optimal scheme for approximate counting and computing partition functions
[Stefankovic, Vempala and Vigoda, IEEE FOCS, 2007.]