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\begin{thebibliography}{}

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\item[] \textbf{The random-cycle model}:

\bibitem[BU07]{bib:bu}
Betz,~V. and Ueltschi,~D.
\newblock{\em Spatial random permutations and infinite cycles}.
\newblock \texttt{arXiv:0711.1188}.

\bibitem[BU08]{bib:bu08}
Betz,~V. and Ueltschi,~D.
\newblock {\em Spatial random permutations with small cycle weights.}
\newblock \texttt{arXiv:0812.0569v1}.

\bibitem[GRU]{bib:gru}
Gandolfo,~D., Ruiz,~J., and Ueltschi,~D.
\newblock {\em On a model of random cycles}.
\newblock \texttt{arXiv:cond-mat/0703315}.
\newblock Statist. Phys. 129, 663-676 (2007).

\bibitem[S\"ut\H{o}1]{bib:suto1}
S\"ut\H{o},~A.
\newblock {\em Percolation transition in the Bose gas.}
\newblock J. Phys. A: Math. Gen. \textbf{26} (1993) 4689-4710.

\bibitem[S\"ut\H{o}2]{bib:suto2}
S\"ut\H{o},~A.
\newblock {\em Percolation transition in the Bose gas II.}
\newblock J. Phys. A: Math. Gen. \textbf{35} (2002) 6995-7002.

\bibitem[U06]{bib:ducycles}
Ueltschi,~D.
\newblock {\em Feynman cycles in the Bose gas.}
\newblock \texttt{arXiv:math-ph/0605002v2}.

\bibitem[U07]{bib:qmath}
Ueltschi,~D.
\newblock {\em The model of interacting spatial permutations and its relation
to the Bose gas.}
\newblock \texttt{arXiv:0712.2443v3}.

%% ----------------------------------------------------------------
\item[] \textbf{Bose-Einstein condensation}:

\bibitem[AEMWC]{bib:boulder}
Anderson,~M.H., Ensher,~J.R., Matthews,~M.R., Wieman,~C.E., and Cornell,~E.A.
\newblock {\em Observation of Bose-Einstein Condensation in a Dilute Atomic
	Vapor}.
\newblock \emph{Science}, vol. 269, issue 5221 (Jul. 14 1995), 198-201.

\bibitem[BBHLV]{bib:baymetal}
Baym,~G., Blaizot,~J.-P., Holzmann,~M., Lalo\"e,~F., and Vautherin,~D.
\newblock {\em Bose-Einstein transition in a dilute interacting gas}.
\newblock \texttt{arXiv:cond-mat/0107129v2}.

\bibitem[AM]{bib:arnoldmoore}
Arnold,~X. and Moore,~X.
\newblock {\em BEC transition temperature of a dilute homogeneous imperfect
	Bose gas}.
\newblock Phys. Rev. Lett. vol. 87, no. 12, Sept. 2001.

\bibitem[BP]{bib:buffetpule}
Buffet,~E. and Pul\`e,~J.V.
\newblock {\em Fluctuation properties of the imperfect Bose gas}.
\newblock J. Math. Phys. vol. 24, no. 6, June 1983.

\bibitem[Ceperley]{bib:ceperley}
Ceperley,~D.M.
\newblock {\em Path integrals in the theory of condensed helium}.
\newblock Rev. Mod. Phys. vol. 67, no. 2, April 1995.

\bibitem[Feynman]{bib:feynman}
Feynman,~R.P.
\newblock {\em Atomic Theory of the $\lambda$ Transition in Helium}.
\newblock The Physical Review, vol. 91, no. 6 (1953).

\bibitem[KPS]{bib:kps}
Kashurnikov,~V.A., Prokof'ev,~N.V., and Svistunov,~B.V.
\newblock {\em Critical temperature shift in weakly interacting Bose gas}.
\newblock Phys. Rev. Lett. vol. 87, no. 12, Aug. 2001.

\bibitem[LSSY]{bib:lssy}
Lieb,~E.H.,
Seiringer,~R.,
Solovej,~J.P.,
and Yngvason,~J.
\newblock {\em The Mathematics of the Bose Gas and its Condensation}.
\newblock Oberwolfach Seminars, vol. 34.
\newblock Birkh\"auser, 2005.

\bibitem[London]{bib:london}
London,~F.
\newblock Phys. Rev. vol. 54, no. 947 (1938).

\bibitem[NL]{bib:nholandau}
Nho,~K. and Landau,~D.P.
\newblock {\em Bose-Einstein condensation temperature of a homogeneous weakly
	interacting Bose gas:  PIMC study}.
\newblock \texttt{arXiv:cond-mat.stat-mech/0404238v1}.

\bibitem[PO]{bib:penons}
Penrose,~O. and Onsager,~L.
\newblock {\em Bose-Einstein Condensation and Liquid Helium}.
\newblock The Physical Review, vol. 104, no. 3 (1956).

%% ----------------------------------------------------------------
\item[] \textbf{Worm algorithm for path-integral Monte Carlo}:

\bibitem[BPS06]{bib:bps06}
Boninsegni,~M., Prokof'ev,~N.V., and Svistunov,~B.V.
\newblock {\em Worm algorithm and diagrammatic Monte Carlo:  A new approach
	to continuous-space path integral Monte Carlo simulations.}
\newblock Physical Review E \textbf{74}, 036701 (2006).

\bibitem[PST98]{bib:pst98}
Prokof'ev,~N.V., Svistunov,~B.V., and Tupitsyn,~I.S.
\newblock {\em Exact, complete, and universal continuous-time worldline Monte
	Carlo approach to the statistics of discrete quantum systems.}
\newblock Journal of Experimental and Theoretical Physics, vol. 87, no. 2
	(1998).

%% ----------------------------------------------------------------
\item[] \textbf{Finite-size scaling for path-integral Monte Carlo}:

\bibitem[GCL97]{bib:gcl97}
Gr\"uter,~P. and Ceperley,~D.
\newblock {\em Critical temperature of Bose-Einstein condensation of
	hard-sphere gases.}
\newblock Physical Review Letters, vol. 79, no. 19 (1997).

\bibitem[HK99]{bib:hk99}
Holzmann,M. and Krauth,~W.
\newblock {\em Transition temperature of the homogeneous, weakly interacting
	Bose gas.}
\newblock Physical Review Letters, vol. 83, no. 14 (1999).

\bibitem[KPS01]{bib:kps01}
Kashurnikov,~V.A., Prokof'ev,~N.V., and Svistunov,~B.V.
\newblock {\em Critical temperature shift in weakly interacting Bose gas}.
\newblock Physical Review Letters, vol. 87, no. 12 (2001).

\bibitem[NL04]{bib:nl04}
Nho,~K. and Landau,~D.P.
\newblock {\em Bose-Einstein condensation temperature of a homogeneous
	weakly interacting Bose gas:  Path integral Monte Carlo study.}
\newblock Physical Review A \textbf{70}, 053614 (2004)

\bibitem[PC87]{bib:pc87}
Pollock,~E.L. and Ceperley,~D.M.
\newblock {\em Path-integral computation of superfluid densities.}
\newblock Physical Review B, vol. 36, no. 16 (1987).

\bibitem[PGP08]{bib:pgp08}
Pilati,~S., Giorgini,~S., and Prokof'ev,~N.V.
\newblock {\em Critical temperature of interacting Bose gases in two and
	three dimensions.}
\newblock Physical Review Letters \textbf{100}, 140405 (2008).

\bibitem[PR92]{bib:pr92}
Pollock,~E.L. and Runge,~K.J.
\newblock {\em Finite-size-scaling analysis of a simulation of the
	${}^4$He superfluid transition}.
\newblock Physical Review B, vol. 46, no. 6 (1992).

%% ----------------------------------------------------------------
\item[] \textbf{Quantum mechanics and statistical mechanics}:

\bibitem[Griffiths]{bib:griffiths}
Griffiths,~D.J.
\newblock {\em Introduction to Quantum Mechanics} (2nd ed.).
\newblock Pearson Prentice Hall, 2005.

\bibitem[Huang]{bib:huang}
Huang,~K.
\newblock {\em Introduction to Statistical Physics}.
\newblock CRC Press, 2001.

\bibitem[Sakurai]{bib:sakurai}
Sakurai,~J.J.
\newblock {\em Modern Quantum Mechanics} (2nd ed.).
\newblock Addison Wesley, 1993.

%% ----------------------------------------------------------------
\item[] \textbf{Analysis}:

\bibitem[HN]{bib:HN}
Hunter,~J. and Nachtergaele,~B.
\newblock {\em Applied Analysis}.
\newblock World Scientific, 2001.

%% ----------------------------------------------------------------
\item[] \textbf{Probability and stochastic processes}:

\bibitem[BS]{bib:bs}
Borodin,~A. and Salminen.,P.
\newblock {\em Handbook of Brownian Motion} (2nd ed.).
\newblock Birkh\"auser, 2002.

\bibitem[BY]{bib:by}
Burdzy,~M. and Yor,~M.
\newblock Personal communication.

\bibitem[Faris]{bib:faris}
Faris,~W.
\newblock {\em The Feynman-Kac formula}.
\newblock Notes for the Arizona Mathematical Physics seminar (2004).

\bibitem[GS]{bib:gs}
Grimmett,~G. and Stirzaker,~D.
\newblock {\em Probability and Random Processes}, 3rd ed.
\newblock Oxford, 2001.

\bibitem[Lawler]{bib:lawler}
Lawler,~G.
\newblock {\em Introduction to Stochastic Processes} (2nd ed.).
\newblock Chapman \& Hall/CRC, 2006.

\bibitem[{\O}ksendal]{bib:oksendal}
{\O}ksendal,~B.
\newblock {\em Stochastic Differential Equations} (6th ed.).
\newblock Springer, 2007.

\bibitem[Yor]{bib:yor}
Yor,~M.
\newblock {\em Some Aspects of Brownian Motion}.
\newblock Birkh\"auser, 1992.

\end{thebibliography}
