"Brownian motion"의 두 판 사이의 차이
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encyclopedia==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* scaling limit of a random walk on a two dimensional grid<br> | * scaling limit of a random walk on a two dimensional grid<br> | ||
| 9번째 줄: | 9번째 줄: | ||
| − | ==heat equation and Brownian motion | + | ==heat equation and Brownian motion== |
* [http://pythagoras0.springnote.com/pages/5650131 열방정식] | * [http://pythagoras0.springnote.com/pages/5650131 열방정식] | ||
| 18번째 줄: | 18번째 줄: | ||
| − | ==Wiener process | + | ==Wiener process== |
* synonym with Brown motion | * synonym with Brown motion | ||
| 29번째 줄: | 29번째 줄: | ||
| − | ==Mandelbrot conjecture | + | ==Mandelbrot conjecture== |
* the Hausdorff dimension of the outer boundary of a planar Brownian motion equals 4=3 | * the Hausdorff dimension of the outer boundary of a planar Brownian motion equals 4=3 | ||
| 41번째 줄: | 41번째 줄: | ||
| − | ==history | + | ==history== |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
| 49번째 줄: | 49번째 줄: | ||
| − | ==related items | + | ==related items== |
* [[Schramm–Loewner evolution (SLE)]] | * [[Schramm–Loewner evolution (SLE)]] | ||
| 60번째 줄: | 60번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia== |
* http://en.wikipedia.org/wiki/Brownian_motion | * http://en.wikipedia.org/wiki/Brownian_motion | ||
| 73번째 줄: | 73번째 줄: | ||
| − | ==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. | ||
| 86번째 줄: | 86번째 줄: | ||
| − | ==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)] | ||
| 99번째 줄: | 99번째 줄: | ||
| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles== |
* [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 | ||
| 116번째 줄: | 116번째 줄: | ||
| − | ==question and answers(Math Overflow) | + | ==question and answers(Math Overflow)== |
* [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 | ||
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
2012년 10월 28일 (일) 14:23 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)
history
encyclopedia==
- http://en.wikipedia.org/wiki/Brownian_motion
- http://en.wikipedia.org/wiki/Wiener_process
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- Paul L´evy: Processus stochastiques et mouvement brownien, 2nd ed. Paris: Gauthier-Villars Paris 1965.
- 2010년 books and articles
- http://gigapedia.info/1/brownian
- http://gigapedia.info/1/brown+motion
- http://gigapedia.info/1/levy
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
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==
- 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
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- Nikolai Roussanov, 2001
- 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
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/