Staff -FUKUSHIMA, Ryoki-

Position Lecturer
E-Mail ryoki (email address: add
My research mainly concerns stochastic processes in radom media. In particular, I have been studying the so-called parabolic Anderson model, which is the diffusion process generated by Schrödinger operator with random potential. The paper [1,2,3] studies the asymptotic behavior of the Feynman-Kac functional, which plays the role of partition function for the diffusion process, corresponding to a potential generated by random displacements of priodic potential. In the other papers [4,5], I proved a precise localization result for the Brownian motion in a Poissonian potentials with long range single site potential. The short range case has been known since long but both result and method are different in the long range case.

1. Brownian survival and Lifshitz tail in perturbed lattice disorder Journal of Functional Analysis, vol. 256, issue 9, 2867-2893 (2009)
2. Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice (joint work with Naomasa Ueki), Annales Henri Poincare, vol. 11, no. 6, 1053-1083 (2010)
3. Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential (joint work with Naomasa Ueki), Journal of Functional Analysis, vol. 260, issue 3, 724-744 (2011)
4. Second order asymptotics for Brownian motion in a heavy tailed Poissonian potential Markov Processes and Related Fields, vol. 17, issue 3, 447-482 (2011)
5. Annealed Brownian motion in a heavy tailed Poissonian potential, to appear in Annals of Probability.