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- Ryoki Fukushima
- 2008

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 sof t 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… (More)

We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions , we show that the total mass of the process grows exponentially in time whenever it survives. More precisely, we prove… (More)

- Ryoki Fukushima
- 2009

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… (More)

We consider the random Schrödinger operator −ε −2 ∆ (d) + ξ (ε) (x), with ∆ (d) the discrete Laplacian on Z d and ξ (ε) (x) are bounded and independent random variables, on sets of the form D ε := {x ∈ Z d : xε ∈ D} for D bounded, open and with a smooth boundary, and study the statistics of the Dirichlet eigenvalues in the limit ε ↓ 0. Assuming Eξ (ε) (x) =… (More)

- RYOKI FUKUSHIMA
- 2009

The survival problem for a diffusing particle moving among random traps is considered. We introduce a simple argument to derive the quenched asymptotics of the survival probability from the Lifshitz tail effect for the associated operator. In particular, the upper bound is proved in fairly general settings and is shown to be sharp in the case of the… (More)

It is proven that the eigenvalue process of Dyson's random matrix process of size two becomes non-Markov if the common coefficient 1/ √ 2 in the non-diagonal entries is replaced by a different positive number.

- Ryoki Fukushima
- 2008

We study two objects concerning the Wiener sausage among Poissonian obstacles. The first is the asymptotics for the replica overlap, which is the intersection of two independent Wiener sausages. We show that it is asymptotically equal to their union. This result confirms that the localizing effect of the media is so strong as to completely determine the… (More)

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