| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Research Abstract |
(1) We defined determinantal processes on spatio-temporal planes as generalizations of determinantal point processes.Using systems of multiple-orthogonal functions, we proved that the noncolliding Brownian motion and the noncolliding Bessel processes are determinantal processes for arbitrary initial configurations with finite numbers of particles, in which all spatio-temporal correlation functions of these processes are determined. We constructed nonequilibrium systems with an infinite number of particles and studied relaxation phenomena to equilibrium states.
(2) We introduced a new notion, a complex Brownian motion representation, for the noncolliding Brownian motion. If the system has this representation, we can prove that it is determinantal and all spatio-temporal correlation functions are obtained.
(3) We studied O'Connell process, which is related with the quantum Toda lattice. We formulated this proces as a generalization of the noncolliding Brownian motion.
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