Deriving Diffusion Processes from Newtonian Mechanics

• Project/Area Number: 18740041
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: University of Tsukuba (2008); Tohoku University (2006-2007)
• Principal Investigator: LIANG Song University of Tsukuba, 大学院・数理物質科学研究科, 准教授 (60324399)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,400,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 確率論 / 拡散過程 / 古典力学系 / 量子場 / $\phi_34$-モデル / ウィック・パワー / フリー量子場 / ウィック指数関数 / Hida分布 / Hoegh-Krohnモデル / ラテス近似 / $ phi_3^4 $-モデル / 部分積分公式 / Levy-Khinchine表現

Research Abstract

一定の初期条件に従う無限個の原子を含む理想気体と呼ばれる環境に分子を入れ、原子達と分子達間の相互作用は古典力学に従うという系について、分子達の挙動を考える。一定の条件の下で、解の一意存在性、そして原子達の質量が0に収束するときの収束性及びその収束先を研究した。本研究の一番のポイントは、原子達が独立であるという今までよく使われていた不自然な仮定を課さないことである。

Research Products

• [Journal Article] A remark on the nonequivalence of the time-zero $ \phi_3^4 $-measure with the free field measure (2008)
  • Author(s): S. Albeverio and S. Liang
  • Journal Title: Markov Processes and Related Fields Volume 14, Issue 1 Pages: 159-164
  • Peer Reviewed
• [Journal Article] A mechanical model of Markov processes (2008)
  • Author(s): S. Kusuoka and S. Liang
  • Journal Title: RIMS Kokyuuroku Bessatsu B6 Pages: 167-176
  • Peer Reviewed
• [Journal Article] A mechanical model of Markov processes (2008)
  • Author(s): S. Kusuoka, S. Liang
  • Journal Title: RIMS Kokyuuroku Bessatsu B6 Pages: 167-176
  • Peer Reviewed
• [Journal Article] A remark on the nonequivalence of the time-zero $ Yphi_3^4 $-measure with the free field measure (2008)
  • Author(s): S. Albeverio, S. Liang
  • Journal Title: Markov Processes and Related Fields 14 Pages: 159-164
  • Peer Reviewed
• [Journal Article] Asymptotic spectral analysis of generalized Erdos-Renyi random graphs, Banach Center publications, institute of Mathematics (2007)
  • Author(s): S. Liang, Nobuaki Obata and Shuji Takahashi
  • Journal Title: Polish Academy of Sciences, Warszawa volume 78 Pages: 211-229
  • Peer Reviewed
• [Journal Article] A note on the renormalized square of free quantum fields in space-time dimension $ d \ge 4 $ (2007)
  • Author(s): S. Albeverio and S. Liang
  • Journal Title: Bulletin des Sciences Mathematique Volume 131, Issue 1 Pages: 1-11
  • Peer Reviewed
• [Journal Article] A note on the renormalized square of free quantum fields in space-time dimension $ d \ge 4 $ (2007)
  • Author(s): S. Alverevio, S. Liang
  • Journal Title: Bulletin des Sciences Mathematique 131 Pages: 1-11
  • Peer Reviewed
• [Journal Article] Different lattice approximations for Hoegh-Krohn's quantum field model (2007)
  • Author(s): S. Liang
  • Journal Title: Stochastic Analysis and Applications: The Abel Symposium 2005 Pages: 493-499
  • Peer Reviewed
• [Journal Article] A note on the renormalized square of free quantum fields in space-time dimension $ d ge 4 $ (2007)
  • Author(s): Sergio Albeverio, Song Liang
  • Journal Title: Bulletin des Sciences Mathematique 131 Pages: 1-11
• [Journal Article] Remark on the integration by parts formula for the $ \phi_3^4 $-quantum field model (2006)
  • Author(s): S. Albeverio, S. Liang and B. Zegarlinski
  • Journal Title: Infinite dimensional analysis, quantum probability and related topics Vol.9, No.1 Pages: 149-154
  • Peer Reviewed
• [Journal Article] Remark on the integration by parts formula for the $ phi_3^4 $-quantum field model (2006)
  • Author(s): S.Albeverio, Song Liang, B.Zegarlinski
  • Journal Title: Infinite dimensional analysis, quantum probability and related topics 9 Pages: 149-154