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Diffstat (limited to 'why_prl.txt')
| -rw-r--r-- | why_prl.txt | 30 |
1 files changed, 9 insertions, 21 deletions
diff --git a/why_prl.txt b/why_prl.txt index 48d3544..8c0eef1 100644 --- a/why_prl.txt +++ b/why_prl.txt @@ -1,21 +1,9 @@ - In our paper we study the extension to complex variables of the -paradigmatic -model of "complex landscape". We believe it is the first paper to study -such complex -"rugged landscapes", a subject of very high interest whose applications -range from deep networks -to optimization. In particular, we introduce and study a matrix model that -has not, to the best of our knowledge -studied previously, and which plays for the fluctuations around complex -saddles -in disordered systems the role played by the well-known semicircle law in -the real ones. -Our work is in line with the beautiful -E *Bogomolny*, O Bohigas, P *Leboeuf* - Physical Review Letters, 1992 -which concerns the roots one random polynomial of high degree, while ours -many of low degree. -We are very sure that sooner or later many new applications of this problem -will appear, as always -has been the case of extending into the complex plane the vision of a real -problem. - +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. |