| Project/Area Number |
24244010
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Kyushu University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
種村 秀紀 千葉大学, 理学(系)研究科(研究院), 教授 (40217162)
舟木 直久 東京大学, 数理(科)学研究科(研究院), 教授 (60112174)
白井 朋之 九州大学, マス・フォア・インダストリ研究所, 教授 (70302932)
熊谷 隆 京都大学, 数理解析研究所, 教授 (90234509)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
KOTANI Shinichi 関西学院大学, 理工学部, 教授 (10025463)
KATORI Makoto 中央大学, 理工学部, 教授 (60202016)
OTOBE Yoshiki 信州大学, 理学部, 准教授 (30334882)
|
|---|
| Research Collaborator |
SHINPDA Masato 奈良女子大学, 理学部, 教授 (50271044)
|
|---|
| Project Period (FY) |
2012-04-01 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| Budget Amount *help |
¥28,470,000 (Direct Cost: ¥21,900,000、Indirect Cost: ¥6,570,000)
Fiscal Year 2015: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2014: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2013: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2012: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000)
|
|---|
| Keywords | 無限粒子系 / 確率力学 / 確率幾何 / ランダム行列 / クーロンポテンシャル / 行列式点過程 / 無限次元確率微分方程式 / 干渉ブラウン運動 / 普遍性 / 行列式測度 / Airy点過程 / Ginibre点過程 / 確率解析 / 対数ポテンシャル / Bessel点過程 / 準Gibbs性 / 対数微分 / ソフトエッジスケーリング |
|---|
| Outline of Final Research Achievements |
We establish a general theory for solving infinite-dimensional stochastic differential equations (ISDE) with symmetry typically appearing in statistical mechanics. In particular, we prove the pathwise uniqueness and the existence of the strong solution under a very general framework. This method is novel, and regards the tail sigma field of the configuration space as a boundary of the ISDE. Furthermore, if the tail sigma field is trivial, then a strong solution exists. If the set of probability-one events is unique, then the pathwise uniqueness of solution holds.
The method is effective for the ISDE with logarithmic interaction potentials, which appear in random matrix theory.
|
