Research on discrete probability models as analysis of algorithms

• Project/Area Number: 21540133
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Fukuoka University of Education
• Principal Investigator: NAKATA Toshio 福岡教育大学, 教育学部, 教授 (10304693)
• Co-Investigator(Kenkyū-buntansha): TAMARI Fumikazu 福岡教育大学, 教育学部, 名誉教授 (70036937)
• Co-Investigator(Renkei-kenkyūsha): KUBO Izumi 広島大学, 理学研究科, 名誉教授 (70022621) ; IKEDA Satoshi 宮崎大学, 工学部, 准教授 (70282796)
• Project Period (FY): 2009-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 離散確率モデル / ポアソンの小数の法則 / 大数の法則 / 中心極限定理 / ネックレス過程 / フェラーのゲーム / 切断和 / 切断確率変数 / 重い裾 / ペテルスブルグのゲーム / 単純ランダムウォーク / 安定分布 / 正則変動 / Schur凸性 / 衝突確率 / 占有問題 / 玉と壷のモデル / Chen-Steinの方法 / ボルツマン抽出 / ボアソンの小数の法則 / 大数の弱法則 / 大数の強法則 / ポアソン近似

Research Abstract

In this research, motivated by analysis of algorithms, we study discrete probability models. Specifically, they mainly contains three topics, namely, "balls and urns with collisions", "necklace processes", and "Feller game and related topics", and we investigate finite structures and limit distributions. For each discrete probability model, we extend known results, and have some limit theorems. Thereby, it seems that the stochastic phenomena of the models may be just solved.

Research Products

• [Journal Article] Another Probabilistic Proof of a Binomial Identity (2014)
  • Author(s): T. Nakata
  • Journal Title: Fibonacci Quart Volume: 52巻, no. 2 Pages: 139-140
  • URL: http://www.fq.math.ca/52-2.html
  • Peer Reviewed
• [Journal Article] The number of collisions for the occupancy problem with unequal probabilities (2014)
  • Author(s): T. Nakata
  • Journal Title: Advances in Applied Probability Volume: 46巻, No.1 Issue: 1 Pages: 168-185
  • DOI: 10.1239/aap/1396360108
  • Peer Reviewed
• [Journal Article] Limit theorems for a generalized Feller game (2014)
  • Author(s): K. Matsumoto and T. Nakata
  • Journal Title: Journal of Applied Probability Volume: 50巻, No. 1 Issue: 1 Pages: 54-63
  • DOI: 10.1239/jap/1363784424
  • Peer Reviewed
• [Journal Article] Integral transforms that preserve Schur convexity with an application to occupancy problem with collisions, Proc (2011)
  • Author(s): T. Nakata
  • Journal Title: 2011 Second International Conference on Networking and Computing, IEEE computer society CS Digital Library Volume: (招待論文) Pages: 352-359
  • DOI: 10.1109/icnc.2011.69
• [Journal Article] On the number of collisions for the balls-and-urns problem with unequal probabilities, Proc (2010)
  • Author(s): T. Nakata
  • Journal Title: 7TH INTERNATIONAL CONFERENCE ON LATTICE PATH COMBINATORICS AND APPLICATIONS, Siena, Italy Pages: 209-212
  • Peer Reviewed
• [Journal Article] On the number of collisions for the balls-and-urns problem with unequal probabilities (2010)
  • Author(s): 中田寿夫
  • Journal Title: Proc.7TH INTERNATIONAL CONFERENCE ON LATTICE PATH COMBINATORICS AND APPLICATIONS Pages: 209-212
  • Peer Reviewed
• [Journal Article] Necklace processes via Polya urns (2009)
  • Author(s): T. Nakata
  • Journal Title: Journal of Applied Probability Volume: 46巻, No. 1 Issue: 1 Pages: 284-295
  • DOI: 10.1239/jap/1238592130
  • Peer Reviewed
• [Journal Article] Approximating the Longest Path Length of a Stochastic DAG by a Normal Distribution in Linear Time (2009)
  • Author(s): E. Ando, T. Nakata, and M. Yamashita
  • Journal Title: Journal of Discrete Algorithms Volume: 7巻, No. 4 Issue: 4 Pages: 420-438
  • DOI: 10.1016/j.jda.2009.01.001
  • Peer Reviewed
• [Journal Article] Necklace processes via Polya urns (2009)
  • Author(s): 中田寿夫
  • Journal Title: Journal of Applied Probability 46 Pages: 284-295
  • Peer Reviewed
• [Journal Article] Approximating the Longest Path Length of a Stochastic DAG by a Normal Distribution in Linear Time (2009)
  • Author(s): E.Ando, T.Nakata, M.Yamashita
  • Journal Title: Journal of Discrete Algorithms 7 Pages: 420-438
  • Peer Reviewed
• [Journal Article] Limit theorems for nonnegative independent random variables with truncation
  • Author(s): T. Nakata
  • Journal Title: Periodica Mathematica Hungarica Volume: (掲載決定)
  • Peer Reviewed
• [Presentation] 切断された非負確率変数列に関する極限定理 (2014)
  • Author(s): 中田寿夫
  • Organizer: 日本数学会2014年度年会
  • Place of Presentation: 学習院大学
  • Year and Date: 2014-03-15
• [Presentation] 切断された非負確率変数列に関する極限定理について (2014)
  • Author(s): 中田寿夫
  • Organizer: 第130回日本数学会九州支部例会
  • Place of Presentation: 琉球大学理学部
  • Year and Date: 2014-02-15
• [Presentation] 期待値の発散するゲームの極限定理について (2013)
  • Author(s): 中田寿夫
  • Organizer: 広島確率論・力学系セミナー
  • Place of Presentation: 広島大学理学部
  • Year and Date: 2013-11-26
• [Presentation] 一般化されたフェラーのゲームの極限定理について (2012)
  • Author(s): 松本啓佑,中田寿夫
  • Organizer: 共同研究集会「無限分解可能過程に関連する諸問題」
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2012-11-08
• [Presentation] The number of collisions for the occupancy problem (2012)
  • Author(s): T. Nakata
  • Organizer: 8th World Congress in Probability and Statistics
  • Place of Presentation: Grand Cevahir Hotel and Convention Center, Istanbul, Tukey
  • Year and Date: 2012-07-11
• [Presentation] Integral transforms that preserve Schur convexity with an application to occupancy problem with collisions (2011)
  • Author(s): T. Nakata
  • Organizer: Workshop on Frontiers of Distributed Computing
  • Place of Presentation: 大阪大学コンベンションセンター
  • Year and Date: 2011-12-01
  • Invited
• [Presentation] Integral Transforms That Preserve Schur Convexity with an Application to Occupancy Problem with Collisions (2011)
  • Author(s): Toshio Nakata
  • Organizer: 2011 Second International Conference on Networking and Computing, 2011
  • Place of Presentation: 大阪大学コンベンションセンター(招待講演)
  • Year and Date: 2011-12-01
• [Presentation] 壷のモデルとその応用 (2011)
  • Author(s): 中田寿夫
  • Organizer: 第124回日本数学会九州支部例会
  • Place of Presentation: 福岡教育大学(特別講演)
  • Year and Date: 2011-02-11
• [Presentation] 壷のモデルとその応用 (2011)
  • Author(s): 中田寿夫
  • Organizer: 第124回日本数学会九州支部例会
  • Place of Presentation: 福岡教育大学(特別講演 招待講演)
  • Year and Date: 2011-02-11
• [Presentation] On the number of collisions for the balls-and-urns problem with unequal probabilities (2010)
  • Author(s): T. Nakata
  • Organizer: 7TH INTERNATIONAL CONFERENCE ON LATTICE PATH COMBINATORICS AND APPLICATIONS
  • Place of Presentation: University of Siena, Italy
  • Year and Date: 2010-07-05
• [Presentation] 衝突の伴う占有問題におけるポアソン近似 (2009)
  • Author(s): 中田寿夫
  • Organizer: 2009年日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] 衝突の伴う占有問題におけるポアソン近似 (2009)
  • Author(s): 中田寿夫
  • Organizer: 2009年日本数学会 秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-24
• [Presentation] 切断された非負確率変数列に関する極限定理について
  • Author(s): 中田寿夫
  • Organizer: 第130回 日本数学会九州支部例会
  • Place of Presentation: 琉球大学理学部
• [Presentation] The number of collisions for the occupancy problem
  • Author(s): Toshio Nakata
  • Organizer: 8th World Congress in Probability and Statistics
  • Place of Presentation: Grand Cevahir Hotel and Convention Center, Istanbul, Tukey
• [Remarks]
  • URL: http://www.fukuoka-edu.ac.jp/~nakata/papers/papers.html