"Brownian motion"의 두 판 사이의 차이

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==introduction==
  
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*  scaling limit of a random walk on a two dimensional grid
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** the limit of random walk as the time and space increments go to zero.
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* Mandelbrot conjecture
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==heat equation and Brownian motion==
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* [http://pythagoras0.springnote.com/pages/5650131 열방정식]
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* [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==
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* synonym with Brown motion
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* example of a Levy process
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==Mandelbrot conjecture==
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* the Hausdorff dimension of the outer boundary of a planar Brownian motion equals 4=3
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* fractal dimension of the frontier of a two dimensional Browninan path is 4/3
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* [[Schramm–Loewner evolution (SLE)]]
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==related items==
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* [[Schramm–Loewner evolution (SLE)]]
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* [[Ito calculus]]
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==encyclopedia==
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* http://en.wikipedia.org/wiki/Brownian_motion
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* http://en.wikipedia.org/wiki/Wiener_process
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==books==
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* Paul L´evy: Processus stochastiques et mouvement brownien, 2nd ed. Paris: Gauthier-Villars Paris 1965.
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==expositions and lecture notes==
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* [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)]
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* [http://www.nber.org/%7Enroussan/thesis/thesis.pdf The Mandelbrot’s Conjecture and Critical Exponents for Brownian Motion]
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** Nikolai Roussanov, 2001
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* [http://www.thehcmr.org/issue2_2/stats_corner.pdf Conformal Invariance in the Scaling Limit of Critical Planar Percolation]
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* [http://stat-www.berkeley.edu/%7Eperes/bmall.pdf An Invitation to Sample Paths of Brownian Motion]
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* http://www.maths.ox.ac.uk/taxonomy/term/1098
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==articles==
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* 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.
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* 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.
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* [http://arxiv.org/abs/math/0506337 On the scaling limit of simple random walk excursion measure in the plane] Michael J. Kozdron, 2005
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* 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.
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* [http://arxiv.org/abs/math/0007042 Critical exponents, conformal invariance and planar Brownian motion][[Wendelin Werner]], 2000
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==question and answers(Math Overflow)==
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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
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[[분류:integrable systems]]
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[[분류:math and physics]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q178036 Q178036]
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===Spacy 패턴 목록===
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* [{'LOWER': 'brownian'}, {'LEMMA': 'motion'}]

2021년 2월 17일 (수) 02:32 기준 최신판

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)


related items



encyclopedia



books

  • Paul L´evy: Processus stochastiques et mouvement brownien, 2nd ed. Paris: Gauthier-Villars Paris 1965.


expositions and lecture notes



articles

question and answers(Math Overflow)

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'brownian'}, {'LEMMA': 'motion'}]
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