"Brownian motion"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) (→메타데이터: 새 문단) |
Pythagoras0 (토론 | 기여) |
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| 5번째 줄: | 5번째 줄: | ||
* Mandelbrot conjecture | * Mandelbrot conjecture | ||
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==heat equation and Brownian motion== | ==heat equation and Brownian motion== | ||
| 14번째 줄: | 14번째 줄: | ||
* [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== | ||
| 41번째 줄: | 41번째 줄: | ||
* [[Ito calculus]] | * [[Ito calculus]] | ||
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| 50번째 줄: | 50번째 줄: | ||
* http://en.wikipedia.org/wiki/Wiener_process | * http://en.wikipedia.org/wiki/Wiener_process | ||
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==books== | ==books== | ||
| 58번째 줄: | 58번째 줄: | ||
* 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== | ||
| 69번째 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== | ||
2020년 12월 28일 (월) 05:20 판
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)
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