From 0ab881e04d8cf6d83917f99d21b9d8bda922b440 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 23 Mar 2021 13:21:34 +0100
Subject: Expanded on Stokes reasoning.

---
 bezout.tex | 19 ++++++++++++++-----
 1 file changed, 14 insertions(+), 5 deletions(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index 902818c..ca0475c 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -85,11 +85,20 @@ $2N$-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 landscape
-of the action in complex space---such as the relative position of saddles and the existence of Stokes lines joining them---must be understood. Such landscapes are in general not random: here
-we follow the standard strategy of computer science by understanding the
-generic features of random instances, expecting that this sheds light on
-practical, nonrandom problems.
+Scorzato_2016_The}.  In order to do this correctly, features of landscape of
+the action 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 critical points, or with a target
+phenomenology that possesses symmetries that restrict the set of critical
+points to few candidates. Given the recent proliferation of `glassiness' in
+condensed matter and high energy physics, it is inevitable that someone will
+study a complex landscape with these methods, and will find old heuristic
+approaches unsuitable. Such landscapes may in general 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 address
+analytic continuation of configuration space 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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