SAKAI, Akira:Creative Research Initiative SOUSEI,Tenure-Track Project Assistant Professor,Applied Mathematics
- Phase transitions, Critical phenomena, Interacting particle systems, Percolation, Ising-Potts model, Lace expansion
- Research Interest:
- Probability theory, Statistical mechanics
- Research Activities:
- My major research field is mathematical physics (probability and statistical mechanics). The problems I have been most interested in are about phase transitions and critical phenomena, as well as associated limit theorems (if there exist). An example that exhibits a phase transition is the Ising model, a model for ferromagnets; it takes on spontaneous magnetization when the temperature of the system is turned down below the critical temperature. In general, critical behavior, i.e., singular behavior of observables, is due to cooperation of infinitely many interacting variables. To understand such phenomena would require development of a theory beyond the standard probability theory for independent random variables. This is a challenging task I would like to contribute to.
The mathematical models I have been working on are the Ising model, self-avoiding walk, percolation, the contact process (a model for the spread of an infection) and random walk with reinforcement.