"Brownian motion"의 두 판 사이의 차이
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* [[Schramm–Loewner evolution (SLE)]] | * [[Schramm–Loewner evolution (SLE)]] | ||
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==related items== | ==related items== | ||
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==encyclopedia== | ==encyclopedia== | ||
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* 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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* 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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* [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]] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
2015년 1월 26일 (월) 21:47 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
- 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