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東京確率論セミナー
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
| 開催情報 | 月曜日 16:00～17:30 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 佐々田槙子、中島秀太（明治大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/2024年度 |
2015年11月30日(月)
16:50-18:20 数理科学研究科棟(駒場) 128号室
Raoul Normand 氏 (中央研究院 數學研究所)
Self-organized criticality in a discrete model of limited aggregation
Raoul Normand 氏 (中央研究院 數學研究所)
Self-organized criticality in a discrete model of limited aggregation
[ 講演概要 ]
We consider a discrete model of coagulation, where a large number of particles are initially given a prescribed number of arms. We successively choose arms uniformly at random and bind them two by two, unless they belong to "large" clusters. In that sense, the large clusters are frozen and become inactive. We study the graph structure obtained, and describe what a typical cluster looks like. We show that there is a fixed time T such that, before time T, a typical cluster is a subcritical Galton-Watson tree, whereas after time T, a typical cluster is a critical Galton-Watson tree. In that sense, we observe a phenomenon called self-organized criticality.
We consider a discrete model of coagulation, where a large number of particles are initially given a prescribed number of arms. We successively choose arms uniformly at random and bind them two by two, unless they belong to "large" clusters. In that sense, the large clusters are frozen and become inactive. We study the graph structure obtained, and describe what a typical cluster looks like. We show that there is a fixed time T such that, before time T, a typical cluster is a subcritical Galton-Watson tree, whereas after time T, a typical cluster is a critical Galton-Watson tree. In that sense, we observe a phenomenon called self-organized criticality.
