WorkshopsComplexity of random smooth functions of many variables
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General smooth Gaussian functions on the sphere in large dimension have very complex landscapes. We give a link between the counting of their critical values or estimating the Euler characteristic of their sub-level sets and random matrix theory. Using this link, we show that those landscapes are very complex. This is motivated by the version at temperature zero of a hard question of statistical mechanics, i.e. the study of Spherical Spin Glasses. We show what we think is the proper invariant to distinguish between two classes of complexity (the 1RSB and Full RSB cases). This is joint work with Antonio Auffinger (Courant) and Jiri Cerny (ETH Zurich).
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Gerard Ben Arous
2011-07-15
14:30:00 - 15:15:00
國際會議廳 , Astronomy and Mathematics Building
General smooth Gaussian functions on the sphere in large dimension have very complex landscapes. We give a link between the counting of their critical values or estimating the Euler characteristic of their sub-level sets and random matrix theory. Using this link, we show that those landscapes are very complex. This is motivated by the version at temperature zero of a hard question of statistical mechanics, i.e. the study of Spherical Spin Glasses. We show what we think is the proper invariant to distinguish between two classes of complexity (the 1RSB and Full RSB cases). This is joint work with Antonio Auffinger (Courant) and Jiri Cerny (ETH Zurich).
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