1.1   非エルミート行列値過程の固有値過程と固有ベクトル・オーバーラップ過程

論文

• Eigenvalues, eigenvector-overlaps, and regularized Fuglede--Kadison determinant of the non-Hermitian matrix-valued Brownian motion  [arXiv], 香取眞理

活動記録

• Numerical study of eigenvector-overlaps and the regularized FK determinants of the non-Hermitian matrix-valued stochastic processes [スライド], 田中雄也, (2023.11.08)

• Rings-to-Disk Transitions in Complex Eigenvalue Processes [スライド], 田中雄也, (2023.08.18)

• ランダム行列のダイナミクス [スライド], 田中雄也, (2023.07.31)

• PDE of the potential field for eigenvalues and eigenvector-overlaps of the non-Hermitian matrix-valued BM [ポスター] [スライド], 田中雄也, (2023.06.05)

1.2   固有値過程と擬固有値過程

論文

• Generalized Eigenspaces and Pseudospectra of Nonnormal and Defective Matrix-Valued Dynamical Systems [arXiv], 森本早織

• Eigenvalue and pseudospectrum processes generated by nonnormal Toepliz matrices with rank 1 perturbations [arXiv], 森本早織

活動記録

• Generalized Eigenspaces and Pseudospectra of Nonnormal and Defective Matrix-Valued Dynamical Systems [スライド], 森本早織, (2024.11.18)

• Eigenvalues and Pseudospectra in Non-Hermitian and Non-Normal Matrix-Valued Processes [スライド], 森本早織,  (2024.08.27)

• Eigenvalues and Pseudospectra in Non-Hermitian and Non-Normal Matrix-Valued Processes [スライド], 森本早織,  (2024.07.11)

• Eigenvalue and pseudospectrum processes generated by nonnormal Toeplitz matrices with perturbation [スライド], 森本早織,  (2024.01.21)

• Eigenvalue and pseudospectrum processes generated by the shift matrix with perturbation [スライド], 森本早織,  (2023.12.06)

• Eigenvalue processes generated by the cyclic permutation matrix and by the shift matrix with perturbation [スライド], 森本早織,  (2023.11.08)

1.3   行列式点過程と超一様性

論文

• Weighted Point Configurations with Hyperuniformity: An Ecological Example and Models [arXiv], 江添綾七

• Local universality of determinantal point processes on Riemannian manifolds [arXiv] [paper], 香取眞理

• Hyperuniformity of the determinantal point processes associated with the Heisenberg group [arXiv] [paper], 香取眞理

• Zeros of the i.i.d. Gaussian Laurent series on an annulus: weighted Szego kernels and permanental-determinantal point processes [arXiv] [paper], 香取眞理

• Partial Isometries, Duality, and Determinantal Point Processes [arXiv] [paper], 香取眞理

• Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes [arXiv] [paper], 香取眞理

• Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures [arXiv] [paper], 越田真史

活動記録

• Algorithms for marked point processes showing hyperuniformity, [スライド], 江添綾七, (2025.01.26)

• 砂漠の藪の分布は超一様か？, [スライド], 江添綾七, (2024.09.11)

• Mathematical modeling of snow dimples, [スライド], 森本早織, (2024.07.24)

• An application of the theory of random point processes; Hyperuniformity of the bushes in deserts, [スライド], 香取眞理, (2024.01.18)

• 砂漠の藪の分布は超一様性を持っているか？[スライド], 江添綾七, (2023.07.31)

書籍

2.1   数理物理学におけるパーコレーションモデルと流行モデル

論文

• Spreading and suppression of infection clusters on the Ginibre continuum percolation clusters [arXiv], 香取眞理

• Continuum percolation and stochastic epidemic models on Poisson and Ginibre point processes [arXiv] [paper], 香取眞理

活動記録

• 多様なグラフ上の感染症ダイナミクスとパーシステントホモロジー [修士論文] [スライド], 石井理矩斗, (2023.11.05) (2024.02.22)

2.2   アリの集団行動と経路選択

論文

• Extinction and Metastability of Pheromone-Roads in Stochastic Models for Foraging Walks of Ants [arXiv], 森本早織

• Switching particle systems for foraging ants showing phase transitions in path selections [arXiv] [paper], 江添綾七

活動記録

• アリの採餌行動模型における経路の存続・消滅転移 [スライド], 森本早織, (2024.09.11)

• Switching Particle Systems for Foraging Ants and Phase Transitions in Path Selections [スライド], 江添綾七, (2024.08.27)

• Switching Particle Systems for Foraging Ants Showing Phase Transitions in Path Selections [スライド], 江添綾七, (2024.07.11)

• Switching particle systems for foraging ants showing phase transitions in path selections [スライド], 江添綾七, (2023.12.06)

• Switching particle systems for foraging ants showing phase transitions in path selections [スライド], 江添綾七, (2023.11.08)

• アリの採餌行動スイッチング模型における経路選択相転移現象 [スライド], 江添綾七, (2023.09.04)

• アリの採餌行動模型における経路の消滅および生成 [スライド], 森本早織, (2023.09.04)

2.3   渋滞・交通流

活動記録

• Classifications and Generalizations of Traffic Flow Models in Statistical Mechanics [スライド], 森本早織, (2023.08.18)

• 交通流モデルの分類と解析 [スライド], 森本早織, (2023.07.31)

2.4   生存競争と植生分布

論文

• Weighted Point Configurations with Hyperuniformity: An Ecological Example and Models [arXiv] [paper], 江添綾七

活動記録

• Algorithms for marked point processes showing hyperuniformity, [スライド], 江添綾七, (2025.01.26)

• 砂漠の藪の分布は超一様か？, [スライド], 江添綾七, (2024.09.11)

• An application of the theory of random point processes; Hyperuniformity of the bushes in deserts, [スライド], 香取眞理, (2024.01.18)

• 砂漠の藪の分布は超一様性を持っているか？[スライド], 江添綾七, (2023.07.31)

2.5   自己駆動系の数理モデル

論文

• Interacting Particle Systems Modeling Self-Propelled Motions [arXiv], 森本早織

活動記録

3.1 多重SLEとガウス自由場の結合

論文

• Coupling of radial multiple SLE with Gaussian free field, and the hydrodynamic limit, [arXiv] , 香取眞理

• On the continuity of half-plane capacity with respect to Caratheodory convergence, [arXiv] [paper], Takuya Murayama 

• Point Processes and Multiple SLE/GFF Coupling [arXiv], 香取眞理

• Three phases of multiple SLE driven by non-colliding Dyson’s Brownian motions, [arXiv] [paper], 香取眞理

• Multiple backward Schramm--Loewner evolution and coupling with Gaussian free field [arXiv] [paper], 越田真史

• Gaussian free fields coupled with multiple SLEs driven by stochastic log-gases [arXiv] [paper], 香取眞理

3.2 流体力学極限

論文

• Coupling of radial multiple SLE with Gaussian free field, and the hydrodynamic limit, [arXiv] , 香取眞理, 笽島千鶴, 鈴木頼杏

活動記録

論文

• On an identity of Chaundy and Bullard. III. Basic and elliptic extensions, [arXiv][paper], 香取眞理

論文

• GICAR algebras and dynamics on determinantal point processes: discrete orthogonal polynomial ensemble case [arXiv], 佐藤僚亮

• Multiplicative Characters and Gaussian Fluctuation Limits, [arXiv], 佐藤僚亮

• Functional equations solving initial-value problems of complex Burgers-type equations for one-dimensional log-gases, [arXiv] [paper], 遠藤大樹

• Free field approach to the Macdonald process, [arXiv] [paper], 越田真史

• The quantum group dual of the first-row subcategory for the generic Virasoro VOA, [arXiv] [paper], 越田真史

活動記録

• 2024年度 卒業研究 発表会, 2024年度卒研生, (2025.01.29)

• 2024年度 白門祭 研究室公開, 2024年度卒研生, (2024.11.03)

• 2023年度 卒業研究 発表会, 2023年度卒研生, (2024.01.30)