"Brownian motion"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| (사용자 2명의 중간 판 6개는 보이지 않습니다) | |||
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==introduction== | ==introduction== | ||
| − | * scaling limit of a random walk on a two dimensional grid | + | * scaling limit of a random walk on a two dimensional grid |
** the limit of random walk as the time and space increments go to zero. | ** the limit of random walk as the time and space increments go to zero. | ||
* Mandelbrot conjecture | * Mandelbrot conjecture | ||
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==heat equation and Brownian motion== | ==heat equation and Brownian motion== | ||
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* [http://stat.math.uregina.ca/%7Ekozdron/Research/UgradTalks/BM_and_Heat/heat_and_BM.pdf http://stat.math.uregina.ca/~kozdron/Research/UgradTalks/BM_and_Heat/heat_and_BM.pdf] | * [http://stat.math.uregina.ca/%7Ekozdron/Research/UgradTalks/BM_and_Heat/heat_and_BM.pdf http://stat.math.uregina.ca/~kozdron/Research/UgradTalks/BM_and_Heat/heat_and_BM.pdf] | ||
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==Wiener process== | ==Wiener process== | ||
| 23번째 줄: | 23번째 줄: | ||
* example of a Levy process | * example of a Levy process | ||
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==Mandelbrot conjecture== | ==Mandelbrot conjecture== | ||
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* [[Schramm–Loewner evolution (SLE)]] | * [[Schramm–Loewner evolution (SLE)]] | ||
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==related items== | ==related items== | ||
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* [[Ito calculus]] | * [[Ito calculus]] | ||
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==encyclopedia== | ==encyclopedia== | ||
| 64번째 줄: | 49번째 줄: | ||
* http://en.wikipedia.org/wiki/Brownian_motion | * http://en.wikipedia.org/wiki/Brownian_motion | ||
* http://en.wikipedia.org/wiki/Wiener_process | * http://en.wikipedia.org/wiki/Wiener_process | ||
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==books== | ==books== | ||
* Paul L´evy: Processus stochastiques et mouvement brownien, 2nd ed. Paris: Gauthier-Villars Paris 1965. | * Paul L´evy: Processus stochastiques et mouvement brownien, 2nd ed. Paris: Gauthier-Villars Paris 1965. | ||
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==expositions and lecture notes== | ==expositions and lecture notes== | ||
* [http://research.microsoft.com/en-us/um/people/schramm/memorial/talk-CDM.ps Scaling Limits of Random Processes and the Outer Boundary of Planar Brownian Motion (2000)] | * [http://research.microsoft.com/en-us/um/people/schramm/memorial/talk-CDM.ps Scaling Limits of Random Processes and the Outer Boundary of Planar Brownian Motion (2000)] | ||
| − | * [http://www.nber.org/%7Enroussan/thesis/thesis.pdf The Mandelbrot’s Conjecture and Critical Exponents for Brownian Motion] | + | * [http://www.nber.org/%7Enroussan/thesis/thesis.pdf The Mandelbrot’s Conjecture and Critical Exponents for Brownian Motion] |
** Nikolai Roussanov, 2001 | ** Nikolai Roussanov, 2001 | ||
* [http://www.thehcmr.org/issue2_2/stats_corner.pdf Conformal Invariance in the Scaling Limit of Critical Planar Percolation] | * [http://www.thehcmr.org/issue2_2/stats_corner.pdf Conformal Invariance in the Scaling Limit of Critical Planar Percolation] | ||
| 95번째 줄: | 69번째 줄: | ||
* http://www.maths.ox.ac.uk/taxonomy/term/1098 | * http://www.maths.ox.ac.uk/taxonomy/term/1098 | ||
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==articles== | ==articles== | ||
| + | * Bodineau, Thierry, Isabelle Gallagher, and Laure Saint-Raymond. “The Brownian Motion as the Limit of a Deterministic System of Hard-Spheres.” arXiv:1305.3397 [math-Ph], May 15, 2013. http://arxiv.org/abs/1305.3397. | ||
* Camia, Federico, Alberto Gandolfi, and Matthew Kleban. “Conformal Correlation Functions in the Brownian Loop Soup.” arXiv:1501.05945 [cond-Mat, Physics:hep-Th, Physics:math-Ph], January 23, 2015. http://arxiv.org/abs/1501.05945. | * Camia, Federico, Alberto Gandolfi, and Matthew Kleban. “Conformal Correlation Functions in the Brownian Loop Soup.” arXiv:1501.05945 [cond-Mat, Physics:hep-Th, Physics:math-Ph], January 23, 2015. http://arxiv.org/abs/1501.05945. | ||
* [http://arxiv.org/abs/math/0506337 On the scaling limit of simple random walk excursion measure in the plane] Michael J. Kozdron, 2005 | * [http://arxiv.org/abs/math/0506337 On the scaling limit of simple random walk excursion measure in the plane] Michael J. Kozdron, 2005 | ||
| 108번째 줄: | 83번째 줄: | ||
* [http://mathoverflow.net/questions/43015/the-conditions-in-the-definition-of-brownian-motion ]http://mathoverflow.net/questions/43015/the-conditions-in-the-definition-of-brownian-motion | * [http://mathoverflow.net/questions/43015/the-conditions-in-the-definition-of-brownian-motion ]http://mathoverflow.net/questions/43015/the-conditions-in-the-definition-of-brownian-motion | ||
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[[분류:integrable systems]] | [[분류:integrable systems]] | ||
[[분류:math and physics]] | [[분류:math and physics]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q178036 Q178036] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'brownian'}, {'LEMMA': 'motion'}] | ||
2021년 2월 17일 (수) 01:32 기준 최신판
introduction
- scaling limit of a random walk on a two dimensional grid
- the limit of random walk as the time and space increments go to zero.
- Mandelbrot conjecture
heat equation and Brownian motion
Wiener process
- synonym with Brown motion
- example of a Levy process
Mandelbrot conjecture
- the Hausdorff dimension of the outer boundary of a planar Brownian motion equals 4=3
- fractal dimension of the frontier of a two dimensional Browninan path is 4/3
- Schramm–Loewner evolution (SLE)
encyclopedia
books
- Paul L´evy: Processus stochastiques et mouvement brownien, 2nd ed. Paris: Gauthier-Villars Paris 1965.
expositions and lecture notes
- Scaling Limits of Random Processes and the Outer Boundary of Planar Brownian Motion (2000)
- The Mandelbrot’s Conjecture and Critical Exponents for Brownian Motion
- Nikolai Roussanov, 2001
- Conformal Invariance in the Scaling Limit of Critical Planar Percolation
- An Invitation to Sample Paths of Brownian Motion
- http://www.maths.ox.ac.uk/taxonomy/term/1098
articles
- Bodineau, Thierry, Isabelle Gallagher, and Laure Saint-Raymond. “The Brownian Motion as the Limit of a Deterministic System of Hard-Spheres.” arXiv:1305.3397 [math-Ph], May 15, 2013. http://arxiv.org/abs/1305.3397.
- Camia, Federico, Alberto Gandolfi, and Matthew Kleban. “Conformal Correlation Functions in the Brownian Loop Soup.” arXiv:1501.05945 [cond-Mat, Physics:hep-Th, Physics:math-Ph], January 23, 2015. http://arxiv.org/abs/1501.05945.
- On the scaling limit of simple random walk excursion measure in the plane Michael J. Kozdron, 2005
- The dimension of the planar Brownian frontier is 4/3 G. F. Lawler, O. Schramm, and W. Werner, Math. Res. Lett., 8:401–411, 2001.
- Critical exponents, conformal invariance and planar Brownian motionWendelin Werner, 2000
question and answers(Math Overflow)
메타데이터
위키데이터
- ID : Q178036
Spacy 패턴 목록
- [{'LOWER': 'brownian'}, {'LEMMA': 'motion'}]