From f4046b1106937531cf2b034f550f311087b4ff82 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 24 Mar 2021 16:00:04 +0100 Subject: Paragraph massaging. --- bezout.tex | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) (limited to 'bezout.tex') diff --git a/bezout.tex b/bezout.tex index ca0475c..151ea2a 100644 --- a/bezout.tex +++ b/bezout.tex @@ -88,17 +88,17 @@ 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. 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 +done for simple actions with few critical points, or for a target +phenomenology with 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 +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 address -analytic continuation of configuration space integrals, understanding the -distribution and spectra of critical points is an essential first step. +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 -- cgit v1.2.3-54-g00ecf