Fixed citations.

2 files changed, 81 insertions, 52 deletions

diff --git a/bezout.bib b/bezout.bib
index f791842..c654568 100644
--- a/bezout.bib
+++ b/bezout.bib
@@ -13,7 +13,7 @@
 
 @article{Antenucci_2015_Complex,
  author = {Antenucci, F. and Crisanti, A. and Leuzzi, L.},
- title = {Complex spherical $2+4$ spin glass: A model for nonlinear optics in random media},
+ title = {Complex spherical {$2+4$} spin glass: A model for nonlinear optics in random media},
  journal = {Physical Review A},
  publisher = {American Physical Society (APS)},
  year = {2015},
@@ -53,6 +53,19 @@
  doi = {10.1214/13-aop862}
 }
 
+@article{Behtash_2017_Toward,
+ author = {Behtash, Alireza and Dunne, Gerald V. and Schäfer, Thomas and Sulejmanpasic, Tin and Ünsal, Mithat},
+ title = {Toward {Picard}–{Lefschetz} theory of path integrals, complex saddles and resurgence},
+ journal = {Annals of Mathematical Sciences and Applications},
+ publisher = {International Press of Boston},
+ year = {2017},
+ number = {1},
+ volume = {2},
+ pages = {95--212},
+ url = {https://doi.org/10.4310%2Famsa.2017.v2.n1.a3},
+ doi = {10.4310/amsa.2017.v2.n1.a3}
+}
+
 @book{Bezout_1779_Theorie,
  author = {Bézout, Etienne},
  title = {Théorie générale des équations algébriques},
@@ -160,6 +173,20 @@
  doi = {10.1051/jp1:1995164}
 }
 
+@article{Cristoforetti_2012_New,
+ author = {Cristoforetti, Marco and Di Renzo, Francesco and Scorzato, Luigi},
+ title = {New approach to the sign problem in quantum field theories: High density {QCD} on a {Lefschetz} thimble},
+ journal = {Physical Review D},
+ publisher = {American Physical Society (APS)},
+ year = {2012},
+ month = {10},
+ number = {7},
+ volume = {86},
+ pages = {074506},
+ url = {https://doi.org/10.1103%2Fphysrevd.86.074506},
+ doi = {10.1103/physrevd.86.074506}
+}
+
 @article{Cugliandolo_1993_Analytical,
  author = {Cugliandolo, L. F. and Kurchan, J.},
  title = {Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model},
@@ -268,6 +295,33 @@
  doi = {10.2307/2371510}
 }
 
+@inproceedings{Scorzato_2016_The,
+ author = {Scorzato, Luigi},
+ title = {The {Lefschetz} thimble and the sign problem},
+ publisher = {Sissa Medialab},
+ year = {2016},
+ month = {7},
+ volume = {251},
+ url = {https://doi.org/10.22323%2F1.251.0016},
+ doi = {10.22323/1.251.0016},
+ booktitle = {Proceedings of The 33rd International Symposium on Lattice Field Theory (LATTICE 2015)},
+ series = {Proceedings of Science}
+}
+
+@article{Tanizaki_2017_Gradient,
+ author = {Tanizaki, Yuya and Nishimura, Hiromichi and Verbaarschot, Jacobus J. M.},
+ title = {Gradient flows without blow-up for {Lefschetz} thimbles},
+ journal = {Journal of High Energy Physics},
+ publisher = {Springer Science and Business Media LLC},
+ year = {2017},
+ month = {10},
+ number = {10},
+ volume = {2017},
+ pages = {100},
+ url = {https://doi.org/10.1007%2Fjhep10%282017%29100},
+ doi = {10.1007/jhep10(2017)100}
+}
+
 @article{Weyl_1912_Das,
  author = {Weyl, Hermann},
  title = {Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)},
@@ -282,57 +336,32 @@
  doi = {10.1007/bf01456804}
 }
 
-
-@article{cristoforetti2012new,
-  title={New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble},
-  author={Cristoforetti, Marco and Di Renzo, Francesco and Scorzato, Luigi and AuroraScience Collaboration and others},
-  journal={Physical Review D},
-  volume={86},
-  number={7},
-  pages={074506},
-  year={2012},
-  publisher={APS}
-}
-@article{tanizaki2017gradient,
-  title={Gradient flows without blow-up for Lefschetz thimbles},
-  author={Tanizaki, Yuya and Nishimura, Hiromichi and Verbaarschot, Jacobus JM},
-  journal={Journal of High Energy Physics},
-  volume={2017},
-  number={10},
-  pages={100},
-  year={2017},
-  publisher={Springer}
-}
-
-
-@article{scorzato2015lefschetz,
-  title={The Lefschetz thimble and the sign problem},
-  author={Scorzato, Luigi},
-  journal={arXiv preprint arXiv:1512.08039},
-  year={2015}
-}
-
-@article{witten2010new,
-  title={A new look at the path integral of quantum mechanics},
-  author={Witten, Edward},
-  journal={arXiv preprint arXiv:1009.6032},
-  year={2010}
-}
-
-@article{witten2011analytic,
-  title={Analytic continuation of Chern-Simons theory},
-  author={Witten, Edward},
-  journal={AMS/IP Stud. Adv. Math},
-  volume={50},
-  pages={347},
-  year={2011}
+@article{Witten_2010_A,
+ author = {Witten, Edward},
+ title = {A new look at the path integral of quantum mechanics},
+ journal = {Surveys in Differential Geometry},
+ publisher = {International Press of Boston},
+ year = {2010},
+ number = {1},
+ volume = {15},
+ pages = {345--420},
+ url = {https://doi.org/10.4310%2Fsdg.2010.v15.n1.a11},
+ doi = {10.4310/sdg.2010.v15.n1.a11}
 }
 
-@article{behtash2015toward,
-  title={Toward Picard-Lefschetz theory of path integrals, complex saddles and resurgence},
-  author={Behtash, Alireza and Dunne, Gerald V and Sch{\"a}fer, Thomas and Sulejmanpasic, Tin and Unsal, Mithat},
-  journal={arXiv preprint arXiv:1510.03435},
-  year={2015}
+@incollection{Witten_2011_Analytic,
+ author = {Witten, Edward},
+ title = {Analytic continuation of {Chern}-{Simons} theory},
+ publisher = {American Mathematical Society},
+ year = {2011},
+ month = {7},
+ volume = {50},
+ pages = {347--446},
+ url = {https://doi.org/10.1090%2Famsip%2F050%2F19},
+ doi = {10.1090/amsip/050/19},
+ booktitle = {Chern-Simons Gauge Theory: 20 Years After},
+ editor = {Andersen, Jørgen E. and Boden, Hans U. and Hahn, Atle and Himpel, Benjamin},
+ series = {AMS/IP Studies in Advanced Mathematics}
 }
 
 
diff --git a/bezout.tex b/bezout.tex
index 8711dd6..d496e52 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -82,7 +82,7 @@ underlying simplicity that is otherwise hidden, and thus sheds light on the orig
 (think, for example, in the radius of convergence of a series).
 
 Deforming a real integration in $N$ variables to a surface of dimension $N$ in
-the $2N$ dimensional complex space has turned out to be necessary for correctly defining and analyzing path integrals with complex action (see \cite{witten2010new,witten2011analytic}), and as a useful palliative for the sign-problem \cite{cristoforetti2012new,tanizaki2017gradient,scorzato2015lefschetz}. 
+the $2N$ dimensional complex space has turned out to be necessary for correctly defining and analyzing path integrals with complex action (see \cite{Witten_2010_A, Witten_2011_Analytic}), and as a useful palliative for the sign-problem \cite{Cristoforetti_2012_New, Tanizaki_2017_Gradient, Scorzato_2016_The}. 
 In order to do this correctly, the features of landscape of the action in complex space must be understood. Such landscapes are in general  not random:   here we propose to follow the strategy of  Computer Science of  understanding the generic features of random instances, expecting that this sheds light on the practical, nonrandom problems.
 
 %Consider, for example, the
@@ -460,7 +460,7 @@ dynamics, are a problem we hope to address in future work.
 
  This paper provides a first step towards the study of a complex landscape with
 complex variables. The next obvious one is to study the topology of the
-critical points, their basins of attraction following  gradient ascent (the Lefschetz thimbles), and descent (the anti-thimbles) \cite{witten2010new,witten2011analytic,cristoforetti2012new,behtash2015toward,scorzato2015lefschetz}, that act as constant-phase integrating `contours'. Locating and counting the saddles that are joined by gradient lines -- the Stokes points, that play an important role in the theory -- is also well within reach of the present-day spin-glass literature techniques.    We anticipate that the
+critical points, their basins of attraction following  gradient ascent (the Lefschetz thimbles), and descent (the anti-thimbles) \cite{Witten_2010_A, Witten_2011_Analytic, Cristoforetti_2012_New, Behtash_2017_Toward, Scorzato_2016_The}, that act as constant-phase integrating `contours'. Locating and counting the saddles that are joined by gradient lines -- the Stokes points, that play an important role in the theory -- is also well within reach of the present-day spin-glass literature techniques.    We anticipate that the
 threshold level, where the system develops a mid-spectrum gap, will play a
 crucial role as it does in the real case.