Random Topology

Randomized topological objects such as simplicial, cubical, and cell complexes have been actively studied in recent years. This research streamline corresponds to higher dimensional generalizations of random graph theory and, in addition, is strongly related to applications in materials science and information and communication systems. We are studying random topology by combining commutative algebra, probability and measure theories.

literature

• Y. Hiraoka and K. Tsunoda. Limit theorems for random cubical homology. Discrete Comput. Geom. 60, 665--687 (2018).
• Y. Hiraoka, T. Shirai, and K. D. Trinh. Limit theorems for persistence diagrams. Ann. Appl. Probab. 28(5), 2740--2780 (2018).
• Y. Hiraoka and T. Shirai. Tutte polynomials and random-cluster models in Bernoulli cell complexes, RIMS Kokyuroku Bessatsu B59, 289--304 (2016).
• Y. Hiraoka and T. Shirai. Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process. Random Structdures ＆ Algorithms 51, 315--340 (2017).
• M. Hino and S. Kanazawa. Asymptotic behavior of lifetime sums for random simplicial complex processes, to appear in J. Math. Soc. Japan. arXiv:1802.00548
• Y. Hiraoka and T. Mikami. Percolation on homology generators in codimension one. arXiv:1809.07490