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diff --git a/why_prl.txt b/why_prl.txt new file mode 100644 index 0000000..8c0eef1 --- /dev/null +++ b/why_prl.txt @@ -0,0 +1,9 @@ +We extend the paradigmatic model of "complex" landscapes to complex variables. +We believe it is the first such study, a subject of interest with applications +from deep networks to optimization. In particular, we introduce an apparently +new matrix model that generalizes the well-known semicircle law for +fluctuations around real saddles in disordered systems. Our work is in line +with Bogomolny, Bohigas & Leboeuf (PRL 1992) concerning roots of one random +polynomial of high degree, while ours many of low degree. Many applications of +this problem will surely appear, as always occurs when extending a real problem +into the complex plane. |