From 4c7e7edb6c7b74ded74a4437d7b15f32c1e6f378 Mon Sep 17 00:00:00 2001 From: "kurchan.jorge" Date: Wed, 9 Dec 2020 15:57:23 +0000 Subject: Update on Overleaf. --- bezout.bib | 11 ++++++++++- bezout.tex | 2 ++ 2 files changed, 12 insertions(+), 1 deletion(-) diff --git a/bezout.bib b/bezout.bib index 5b61d1e..51df35d 100644 --- a/bezout.bib +++ b/bezout.bib @@ -11,7 +11,16 @@ url = {https://doi.org/10.1007%2Fjhep12%282016%29071}, doi = {10.1007/jhep12(2016)071} } - +@article{bogomolny1992distribution, + title={Distribution of roots of random polynomials}, + author={Bogomolny, Eugene and Bohigas, Oriol and Leboeuf, Patricio}, + journal={Physical Review Letters}, + volume={68}, + number={18}, + pages={2726}, + year={1992}, + publisher={APS} +} @article{Antenucci_2015_Complex, author = {Antenucci, F. and Crisanti, A. and Leuzzi, L.}, title = {Complex spherical {$2+4$} spin glass: A model for nonlinear optics in random media}, diff --git a/bezout.tex b/bezout.tex index 9dc6cc8..03fad88 100644 --- a/bezout.tex +++ b/bezout.tex @@ -69,6 +69,8 @@ complex variables, and the roots are simple all the way (we shall confirm this), variables minima of functions appear and disappear, and this procedure is not possible. The same idea may be implemented by performing diffusion in the $J$'s, and following the roots, in complete analogy with Dyson's stochastic dynamics. +This study also provides a complement to the work on the distribution of zeroes of random polynomials \cite{bogomolny1992distribution}. + Let us go back to our model. For the constraint we choose here $z^2=N$, rather than $|z|^2=N$, in order to preserve the holomorphic nature -- cgit v1.2.3-70-g09d2