Brownian motion

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

• 열방정식
• http://stat.math.uregina.ca/~kozdron/Research/UgradTalks/BM_and_Heat/heat_and_BM.pdf

 

 

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

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• Schramm–Loewner evolution (SLE)
• Ito calculus

 

 

 

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)

• [1]http://mathoverflow.net/questions/43015/the-conditions-in-the-definition-of-brownian-motion
• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=