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2012년 11월 1일 (목) 12:07 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/
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/