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講演会
過去の記録 ～04/16｜次回の予定｜今後の予定 04/17～
2011年12月09日(金)
10:40-11:30 数理科学研究科棟(駒場) 122号室
Erwin Bolthausen 氏 (University of Zurich)
An iterative construction of solutions of the TAP equation (ENGLISH)
Erwin Bolthausen 氏 (University of Zurich)
An iterative construction of solutions of the TAP equation (ENGLISH)
[ 講演概要 ]
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.
