"Regularity structure in stochastic PDE"의 두 판 사이의 차이
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imported>Pythagoras0 (section 'expositions' updated) |
Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 4개는 보이지 않습니다) | |||
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==introduction== | ==introduction== | ||
| + | * These lecture notes grew out of a series of lectures given by the second named author in short courses in Toulouse, Matsumoto, and Darmstadt. | ||
| + | * The main aim is to explain some aspects of the theory of "Regularity structures" developed recently by Hairer in arXiv:1303.5113 . | ||
| + | * This theory gives a way to study well-posedness for a class of stochastic PDEs that could not be treated previously. | ||
| + | * Prominent examples include the KPZ equation as well as the dynamic <math>\Phi^4_3</math> model. Such equations can be expanded into formal perturbative expansions. | ||
| + | * Roughly speaking the theory of regularity structures provides a way to truncate this expansion after finitely many terms and to solve a fixed point problem for the "remainder". | ||
| + | * The key ingredient is a new notion of "regularity" which is based on the terms of this expansion. | ||
| + | |||
==expositions== | ==expositions== | ||
| 5번째 줄: | 12번째 줄: | ||
* Martin Hairer, The motion of a random string, arXiv:1605.02192 [math.PR], May 07 2016, http://arxiv.org/abs/1605.02192 | * Martin Hairer, The motion of a random string, arXiv:1605.02192 [math.PR], May 07 2016, http://arxiv.org/abs/1605.02192 | ||
| + | [[분류:migrate]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q28401890 Q28401890] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'regularity'}, {'LEMMA': 'structure'}] | ||
2021년 2월 17일 (수) 01:31 기준 최신판
introduction
- These lecture notes grew out of a series of lectures given by the second named author in short courses in Toulouse, Matsumoto, and Darmstadt.
- The main aim is to explain some aspects of the theory of "Regularity structures" developed recently by Hairer in arXiv:1303.5113 .
- This theory gives a way to study well-posedness for a class of stochastic PDEs that could not be treated previously.
- Prominent examples include the KPZ equation as well as the dynamic \(\Phi^4_3\) model. Such equations can be expanded into formal perturbative expansions.
- Roughly speaking the theory of regularity structures provides a way to truncate this expansion after finitely many terms and to solve a fixed point problem for the "remainder".
- The key ingredient is a new notion of "regularity" which is based on the terms of this expansion.
expositions
- Ajay Chandra, Hendrik Weber, Stochastic PDEs, Regularity Structures, and Interacting Particle Systems, arXiv:1508.03616 [math.AP], August 14 2015, http://arxiv.org/abs/1508.03616
- Martin Hairer, The motion of a random string, arXiv:1605.02192 [math.PR], May 07 2016, http://arxiv.org/abs/1605.02192
메타데이터
위키데이터
- ID : Q28401890
Spacy 패턴 목록
- [{'LOWER': 'regularity'}, {'LEMMA': 'structure'}]