From 7bc5969c319a760c3259455e5bd24d1694ba1def Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 29 Dec 2020 19:15:47 +0100
Subject: Fixed citations.

---
 bezout.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'bezout.tex')

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.
 
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