Sharp bound of the spectral gap for particle systems

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K03267
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Niigata University
• Principal Investigator: Nagahata Yukio 新潟大学, 自然科学系, 教授 (50397725)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: spectral gap / zero-range process / martingale method

Outline of Final Research Achievements

We study the sharp order estimate of the spectral gap for zero-range process. As a previous research, by using Yau's martingale method, the spectral gap estimate for the zero-range process is discussed. In this research, the spectral gap does not depends on the density of particles. It is also desired that we improve this method to the density depending spectral gap estimate. However we should add some technical assumption on the jump rate for zero-range process, we improve this method.

Free Research Field

確率論

Academic Significance and Societal Importance of the Research Achievements

確率過程論においてスペクトルギャップはその確率過程の重要な基本的特性量であり、その詳細評価はそれだけでも十分な意味を持ちますが、特に粒子系の確率過程で、時間―空間に関するスケール極限を行う場合にはスペクトルギャップの評価を必要とします。興味深いスケール極限に関する結果の中には、スペクトルギャップの評価を仮定すれば成り立つとするものもあり、今回の結果により適用範囲が増えたことになり意味のある結果となります。