
First and foremost, thanks go to co-advisors Daniel Ueltschi and Tom Kennedy.
Much of what I have learned in this project has been learned through them;
their patience has been endless and their knowledge has been irreplaceable.

My work in spring 2008 and spring 2009 was supported by research assistantships
through National Science Foundation grant DMS-0601075.  Summer 2009, fall 2009,
and spring 2010 research assistantships were funded by the University of
Arizona Department of Mathematics NSF VIGRE (Vertical InteGration in Research
and Education) grant.

The July 2008 Summer School on Current Topics in Mathematical Physics at the
Erwin Schr\"odinger Institute in Vienna, organized by Christian Hainzl and
Robert Seiringer, was my first mathematical physics conference.  There, I made
several valuable contacts; I also benefited from extended collaboration time
with Daniel Ueltschi.  The March 2009 school on Entropy and the Quantum in
Tucson, organized by Daniel Ueltschi and Bob Sims, allowed further networking
opportunities.  In particular, Volker Betz posed a question on upper and lower
bounds for Brownian-bridge interactions, and gave unexpected advice on software
architecture.  Bob Sims' June 2009 workshop on Quantum Spin Systems and
Applications in Quantum Computation in Tucson, at which I presented ongoing
results of a side project in three-dimensional percolation, gave me valuable
feedback on finite-size scaling which I was able to apply to my dissertation
work.  Daniel Gandolfo and Jean Ruiz, of the Universit\'e de Marseille and the
Centre National de la Recherche Scientifique, respectively, were kind enough to
host me for three days in July 2009 before a conference in Berlin.  There,
Gandolfo and Ueltschi gave me useful advice on my writing.  Ueltschi's
challenging questions on autocorrelation led me to write appendix
\ref{appx:eta}.  Gandolfo and I discussed computational methods including
lookup-table methods for the true Bose-gas interactions and the inapplicability
of fourth-order-cumulant methods to our problem.  The July 2009 conference on
Stochastic Processes and Their Applications in Berlin allowed me to present my
work to a probabilist audience.  The February 2010 workshop of the Center for
Simulational Physics at the University of Georgia provided invaluable contacts
for me, including key ideas for presentation graphics due to Joan Adler of
Technion, and a likely solution to the band-update problem due to Friederike
Schmid of the University of Mainz.

Two reviewers for the Journal of Statistical Physics provided expert
reassurance regarding the correctness of the methodology presented in an
abbreviated version of this dissertation, while also helping to clarify the
exposition.  My committee members --- Tom, Daniel, Kevin, and Rabi --- likewise
read this dissertation carefully and offered thoughtful suggestions for
improvement.

Small-scale simulational processing for this project was done on the
8-processor chivo cluster at the University of Arizona Department of
Mathematics.  Large-scale processing was done on the massively parallel ICE
cluster at the University of Arizona High Performance Computing center.

The University of Arizona Department of Mathematics has been a supportive,
stimulating environment in which I have been fortunate to spend the last five
years.  After graduation I will miss this department; I will take its best
practices with me.

Most importantly, I thank my wife, Sarah, for her patience and support.  She
and I have labored side by side as she progresses through a doctoral program in
anthropology.  Now, it's her turn to write a dissertation.

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