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

Activity

• 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

• 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

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

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

Activity

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

• Particle Systems for Foraging Ants and Annihilation and Creation of Paths, Saori Morimoto

2.3   Traffic Flow and Jamming

Activity

Paper

• 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 

Paper

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

• 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