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| -rw-r--r-- | bezout.tex | 14 |
1 files changed, 7 insertions, 7 deletions
@@ -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 |