Ryoki Fukushima
Kyoto University
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Featured researches published by Ryoki Fukushima.
Journal of Functional Analysis | 2009
Ryoki Fukushima
Abstract We consider the annealed asymptotics for the survival probability of Brownian motion among randomly distributed traps. The configuration of the traps is given by independent displacements of the lattice points. We determine the long time asymptotics of the logarithm of the survival probability up to a multiplicative constant. As applications, we show the Lifshitz tail effect of the density of states of the associated random Schrodinger operator and derive a quantitative estimate for the strength of intermittency in the parabolic Anderson problem.
Annales Henri Poincaré | 2010
Ryoki Fukushima; Naomasa Ueki
The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at the infimum of the spectrum is investigated. The leading term is determined when the decay of the single site potential is slow. The leading term depends only on the classical effect from the scalar potential. To the contrary, the quantum effect appears when the decay of the single site potential is fast. The corresponding leading term is estimated and the leading order is determined. In the multidimensional cases, the leading order varies in different ways from the known results in the Poisson case. The same problem is considered for the negative potential. These estimates are applied to investigate the long time asymptotics of Wiener integrals associated with the random potentials.
Journal of Functional Analysis | 2011
Ryoki Fukushima; Naomasa Ueki
Abstract The parabolic Anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied. The moment asymptotics of the total mass of the solution is derived. The results show that the total mass of the solution concentrates on a small set in the space of configuration.
Journal of Statistical Physics | 2008
Ryoki Fukushima
We consider the Wiener sausage among Poissonian obstacles. The obstacle is called hard if Brownian motion entering the obstacle is immediately killed, and is called soft if it is killed at certain rate. It is known that Brownian motion conditioned to survive among obstacles is confined in a ball near its starting point. We show the weak law of large numbers, large deviation principle in special cases and the moment asymptotics for the volume of the corresponding Wiener sausage. One of the consequence of our results is that the trajectory of Brownian motion almost fills the confinement ball.
Journal of Theoretical Probability | 2014
Ryoki Fukushima; Naoki Kubota
We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.
Journal of Statistical Physics | 2015
Francis Comets; Ryoki Fukushima; Shuta Nakajima; Nobuo Yoshida
We study asymptotics of the free energy for the directed polymer in random environment. The polymer is allowed to make unbounded jumps and the environment is given by Bernoulli variables. We first establish the existence and continuity of the free energy including the negative infinity value of the coupling constant
Stochastic Processes and their Applications | 2018
Jean-Dominique Deuschel; Ryoki Fukushima
Annals of Probability | 2013
Ryoki Fukushima
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arXiv: Probability | 2010
Ryoki Fukushima
arXiv: Probability | 2014
Marek Biskup; Ryoki Fukushima; Wolfgang Koenig
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