From b113e5a975e849926b11dd98cdfc94ca972de914 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 24 Mar 2021 16:26:40 +0100
Subject: Line length...

---
 bezout.tex | 30 ++++++++++++++++--------------
 1 file changed, 16 insertions(+), 14 deletions(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 2a34bbf..ed03a28 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -80,23 +80,25 @@ plane often uncovers underlying simplicity that is otherwise hidden, shedding
 light on the original real problem, e.g., as in the radius of convergence of a
 series.
 
-Finally, deforming an integral in $N$ real variables to a surface of dimension $N$ in
-$2N$-dimensional complex space has turned out to be necessary for correctly
-defining and analyzing path integrals with complex action (see
+Finally, deforming an integral in $N$ real variables to a surface of dimension
+$N$ in $2N$-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, features of the action's landscape in complex space---such as the relative position of saddles and the
+Scorzato_2016_The}.  In order to do this correctly, features of the action's
+landscape in complex space---such as the relative position of saddles and the
 existence of Stokes lines joining them---must be understood.  This is typically
-done for simple actions with few saddles, or for a target
-phenomenology with symmetries that restrict the set of saddles to few candidates. Given the recent proliferation of `glassiness' in
-condensed matter and high energy physics, it is inevitable that someone will
-want to apply these methods to a system with a complex landscape, and will find
-they cannot use approaches that rely on such assumptions. Their landscape may not be random: here we
-follow the standard strategy of computer science by understanding the generic
-features of random instances of a simple case, expecting that this sheds light
-on practical, nonrandom problems. While in this paper we do not yet address
-analytic continuation of integrals, understanding the distribution and spectra
-of critical points is an essential first step.
+done for simple actions with few saddles, or for a target phenomenology with
+symmetries that restrict the set of saddles to few candidates. Given the recent
+proliferation of `glassiness' in condensed matter and high energy physics, it
+is inevitable that someone will want to apply these methods to a system with a
+complex landscape, and will find they cannot use approaches that rely on such
+assumptions. Their landscape may not be random: here we follow the standard
+strategy of computer science by understanding the generic features of random
+instances of a simple case, expecting that this sheds light on practical,
+nonrandom problems. While in this paper we do not yet address analytic
+continuation of integrals, understanding the distribution and spectra of
+critical points is an essential first step.
 
 Returning to our problem, the spherical constraint is enforced using the method
 of Lagrange multipliers: introducing $\epsilon\in\mathbb C$, our constrained
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