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無限解析研究部門（梶野 直孝）
Showing the original Japanese · View translation
フラクタルの上で、Laplacianと確率過程を解析する、確率論の研究室。
AboutAbout the lab
フラクタルの上の確率過程を解き明かす。
梶野研究室は、
フラクタルは、
そう
近年は、
Key terms
- フラクタル
- 拡大しても
全体と 似た 形が 細部に くり返し現れる 図形。 シェルピンスキーの ガスケットが 代表例 - Laplacian
- 関数の
値ので こぼこを 測る 微分作用素。 熱の 広がり方を 表す方 程式に 現れる - 熱核
- 1点から
出た 熱が、 時刻ごとにどの 場所へ どれだけ広がるかを 表す関数。 確率過程の 推移確率密度に あたる
ResearchResearch themes
フラクタルと
*Illustrative image劣Gauss型熱核評価とエネルギー測度
Euclid自己相似フラクタルで
*Illustrative image擬等角構造と高次元のSierpiński gasket
一方、
*Illustrative imageLiouville量子重力とLiouville Brown運動
曲面上の
*Illustrative image自己等角フラクタルのLaplacian
Klein群の
MembersFaculty
- Associate Professor梶野 直孝
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Pseudo Kleinian OpenCL K 002” PantheraLeo1359531 / CC BY-SA 4.0 (cropped)
- 劣Gauss型熱核評価と
エネルギー測度: “Apollonian gasket symmetrical 3” Cmglee / CC BY-SA 4.0 (cropped) - 擬等角構造と
高次元の Sierpiński gasket: “Sierpinski Triangle mod 3” Kabrick1 / CC BY 4.0 (cropped) - Liouville量子重力と
Liouville Brown 運動: “Discrete Gaussian free field on 60 x 60 square grid” Samuelswatson / Public domain (cropped) - 自己等角フラクタルの
Laplacian: “Julia set (highres 01)” Solkoll / Public domain (cropped) - Related lab (無限解析研究部門
（CROYDON, David） ): “Schramm-Loewner Evolution” Tesseract16 / CC0 (cropped) - Related lab (無限解析研究部門
（星 裕一郎） ): “Kleinian group limit set on sphere” Adam majewski / CC BY-SA 4.0 (cropped) - Related lab (無限解析研究部門
（望月 新一） ): “Kyoto University RIMS” KATSURA Roen / CC BY 3.0 (cropped) - Related lab (無限解析研究部門
（玉川 安騎男） ): “Klein-map” PSL27 / CC BY-SA 4.0 (cropped)
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