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authorJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-21 12:45:16 +0100
committerJaron Kent-Dobias <jaron@kent-dobias.com>2020-12-21 12:45:16 +0100
commitc93686b645159f8ed0112c38b439606503d04cd4 (patch)
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Revised our 'why' statement to 100 words.
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- 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.