Japanese page is HERE. ( ←日本語はこちら。)
Position:
Assistant Professor
Affiliation:
Department of Mathematics
Faculty of Education
Kagoshima University
Address:
1-20-6 Korimoto, Kagoshima 890-0065, Japan
e-mail
Please replace the Japanese characters with at.
s-osada{ぬ｝edu.kagoshima-u.ac.jp
s_osada｛め} outlook.com
🔗Access info (Please translate)
Keywords: Probability theory, point processes, infinite particle systems, ergodic theory, Bernoulli property, Ornstein's isomorphism theory
My research is in probability theory, with a particular focus on point processes consisting of infinitely many particles.
I view point processes from three broad structural perspectives: kernel-based systems, potential-based systems, and zero sets. I have worked on determinantal point processes (DPPs), whose correlation structures are described by kernel functions; zero point processes of Gaussian analytic functions (GAFs); and Coulomb systems, in which interactions between particles are described by potentials. I am interested in how these different structures are related and to what extent they determine the properties of point processes.
A central theme of my research is the probabilistic structure and phenomena that emerge specifically in the infinite-particle regime. I study infinite point processes and their associated dynamics through such structures as limits of finite-particle systems, Gibbsian descriptions, correlation structures, and infinite-dimensional stochastic processes.
I am also interested in understanding point processes from the viewpoint of ergodic theory. In particular, I would like to understand how close interacting point processes and their dynamics are to Poisson systems, and in what sense they differ. I approach these questions through the Bernoulli property, factor structures, and Ornstein's isomorphism theory. My interests include not only static point configurations but also the time evolution and long-time behavior of infinite particle systems.