A study on linear pseudorandom number generators with long period

• Project/Area Number: 20740050
• 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: Yamagata University
• Principal Investigator: NISHIMURA Takuji Yamagata University, 理学部, 准教授 (90333947)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2010: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 擬似乱数生成法 / 重み分布 / 初期値 / 擬似乱数生成 / 有限体 / 擬似乱数の合成 / 重み分布検定

Research Abstract

We studied pseudorandom number generators based on linear recurrences over finite fields. Pseudorandom numbers are indispensable tools for Monte Carlo simulations. Linear pseudorandom number generators are often used in the simulations. In this research, we studied properties of linear pseudorandom number generators in the weight distribution tests. Relationship between the form of the recurrence of generators and their initial states are studied. We analyzed also relationship between the form of the recurrence and their outputs in the weight distribution tests. We constructed pseudorandom number generators with maximally equidistribution property.

Research Products

• [Journal Article] New inputs and methods for Markov chain quasi-Monte Carlo (2010)
  • Author(s): S.Chen, M.Matsumoto, T.Nishimura, A.B.Owen
  • Journal Title: Monte Carlo and quasi-Monte Carlo Methods 受理
  • Peer Reviewed
• [Presentation] Exact Methods for Evaluating Linear Pseudorandom Number Generators (2008)
  • Author(s): 西村拓士
  • Organizer: Monte Carlo and Quasi-Monte Carlo Methods 2008
  • Place of Presentation: モントリオール大学
  • Year and Date: 2008-07-10
• [Presentation] Exact Methods for Evaluating Linear Pseudorandom Number Generators (2008)
  • Author(s): 西村拓士
  • Organizer: Monte Carlo and Quasi-Monte Carlo Methods 2008
  • Place of Presentation: モントリオール大学(カナダ)
  • Year and Date: 2008-07-10