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2022 Fiscal Year Final Research Report

Mean-field theory for random geometric graph and its application to mathematical models

Research Project

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Project/Area Number 19K14613
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
Research InstitutionTokyo Institute of Technology (2021-2022)
Nagoya Institute of Technology (2019-2020)

Principal Investigator

Takabe Satoshi  東京工業大学, 情報理工学院, 准教授 (60804218)

Project Period (FY) 2019-04-01 – 2023-03-31
Keywords情報統計力学 / ランダムグラフ / ランダム幾何グラフ / アドホックネットワーク
Outline of Final Research Achievements

In this study, we aimed to construct an mean-field theory for mathematical models on random geometric graphs defined on the Euclidean space, based on the statistical mechanics for disordered systems. As a result, we have stduied the following research topics: (1) the statistical-mechanical analysis of the degree correlations applicable to generalized random geometric graphs, a wider class of random geometric graphs, and (2) mean-field analysis of the robustness in ad-hoc wireless communication models. Especially, the latter enables the estimation of robustness on graphs with finite nodes, which predicts numerical simulations well.

Free Research Field

情報統計力学

Academic Significance and Societal Importance of the Research Achievements

ランダム系の統計力学は幾何構造を有しないランダムグラフに対してよく適用されていたが、本研究ではそれをランダム幾何グラフへ応用することで、新たな解析手法の確立に寄与したといえる。また、ランダム幾何グラフは無線通信や感染症等の数理モデルとして自然に現れることから、本研究で提案する解析手法はこれらの応用分野にも適用可能であると考えられる。

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Published: 2024-01-30  

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