Research Subjects

1.1   Eigenvector-Overlap Processes of Non-Hermitian Matrix-valued Stochastic Processes

Paper

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

Activity

• Numerical study of eigenvector-overlaps and the regularized FK determinants of the non-Hermitian matrix-valued stochastic processes [slide], Yuya Tanaka, (2023.11.08)

• Rings-to-Disk Transitions in Complex Eigenvalue Processes [slide], Yuya Tanaka, (2023.08.18)

• PDE of the potential field for eigenvalues and eigenvector-overlaps of the non-Hermitian matrix-valued BM [poster] [slide], Yuya Tanaka, (2023.06.05)

1.2   Eigenvalue and Pseudospectrum Processes

Paper

• Generalized Eigenspaces and Pseudospectra of Nonnormal and Defective Matrix-Valued Dynamical Systems [arXiv], Saori Morimoto

• Eigenvalue and pseudospectrum processes generated by nonnormal Toepliz matrices with rank 1 perturbations [arXiv], Saori Morimoto

Activity

• Generalized Eigenspaces and Pseudospectra of Nonnormal and Defective Matrix-Valued Dynamical Systems [slide], Saori Morimoto, (2024.11.18)

• Eigenvalues and Pseudospectra in Non-Hermitian and Non-Normal Matrix-Valued Processes [slide], Saori Morimoto,  (2024.08.27)

• Eigenvalues and Pseudospectra in Non-Hermitian and Non-Normal Matrix-Valued Processes [slide], Saori Morimoto,  (2024.07.11)

• Eigenvalue and pseudospectrum processes generated by the shift matrix with perturbation [slide], Saori Morimoto,  (2023.12.06)

• Eigenvalue processes generated by the cyclic permutation matrix and by the shift matrix with perturbation [slide], Saori Morimoto,  (2023.11.08)

1.3   Determinantal Point Processes and Hyperuniformity

Paper

• Weighted Point Configurations with Hyperuniformity: An Ecological Example and Models [arXiv], Ayana Ezoe

• Local universality of determinantal point processes on Riemannian manifolds [arXiv] [paper], Makoto Katori

• Hyperuniformity of the determinantal point processes associated with the Heisenberg group [arXiv] [paper], Makoto Katori

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

• Partial Isometries, Duality, and Determinantal Point Processes [arXiv] [paper], Makoto Katori

• Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes [arXiv] [paper], Makoto Katori

• Pfaffian Point Processes from Free Fermion Algebras: Perfectness and Conditional Measures [arXiv] [paper], Shinji Koshida

Activity

• Mathematical modeling of snow dimples, [slide], Saori Morimoto, (2024.07.24)

Book

2.1   Percolation Models and Epidemic Models in Mathematical Physics

Paper

• Spreading and suppression of infection clusters on the Ginibre continuum percolation clusters [arXiv], Makoto Katori

• Continuum percolation and stochastic epidemic models on Poisson and Ginibre point processes [arXiv] [paper], Makoto Katori

2.2   Group Behavior and Path Selection of Ants

Paper

• Extinction and Metastability of Pheromone-Roads in Stochastic Models for Foraging Walks of Ants [arXiv], Saori Morimoto

• Switching particle systems for foraging ants showing phase transitions in path selections [arXiv], [paper], Ayana Ezoe

Activity

• Switching Particle Systems for Foraging Ants and Phase Transitions in Path Selections [slide], Ayana Ezoe, (2024.08.27)

• Switching Particle Systems for Foraging Ants Showing Phase Transitions in Path Selections [slide], Ayana Ezoe, (2024.07.11)

• Switching particle systems for foraging ants showing phase transitions in path selections [slide], Ayana Ezoe, (2023.12.06)

• Switching particle systems for foraging ants showing phase transitions in path selections [slide], Ayana Ezoe, (2023.11.08)

2.3   Traffic Flow and Jamming

Activity

• Classifications and Generalizations of Traffic Flow Models in Statistical Mechanics [slide], Saori Morimoto, (2023.08.18)

2.4   Competition for Survival in Biological Populations

Paper

• Weighted Point Configurations with Hyperuniformity: An Ecological Example and Models [arXiv] [paper], Ayana Ezoe

2.5   Mathematical Models of Self-Propelled Systems

Paper

3.1   Coupling of Multiple SLE and GFF

Paper

• Coupling of radial multiple SLE with Gaussian free field, and the hydrodynamic limit, [arXiv] ,  Makoto Katori

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

• Point Processes and Multiple SLE/GFF Coupling [arXiv], Makoto Katori

• Three phases of multiple SLE driven by non-colliding Dyson’s Brownian motions, [arXiv] [paper], Makoto Katori, Shinji Koshida

• Multiple backward Schramm--Loewner evolution and coupling with Gaussian free field [arXiv] [paper], Shinji Koshida

• Gaussian free fields coupled with multiple SLEs driven by stochastic log-gases [arXiv] [paper], Makoto Katori, Shinji Koshida

3.2   Hydrodynamic Limits

Paper

• Coupling of radial multiple SLE with Gaussian free field, and the hydrodynamic limit, [arXiv] ,  Makoto Katori, Chizuru Soukejima, Raian Suzuki

Activity

Paper

• On an identity of Chaundy and Bullard. III. Basic and elliptic extensions, [arXiv][paper], Makoto Katori

Paper

• GICAR algebras and dynamics on determinantal point processes: discrete orthogonal polynomial ensemble case [arXiv], Ryosuke Sato

• Multiplicative Characters and Gaussian Fluctuation Limits, [arXiv], Ryosuke Sato

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

• Free field approach to the Macdonald process, [arXiv] [paper], Shinji Koshida

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