Localization for the random displacement model
We prove spectral and dynamical localization for the multidimensional random displacement
model near the bottom of its spectrum by showing that the approach through multiscale …
model near the bottom of its spectrum by showing that the approach through multiscale …
From the Lifshitz tail to the quenched survival asymptotics in the trapping problem
R Fukushima - 2009 - projecteuclid.org
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 …
introduce a simple argument to derive the quenched asymptotics of the survival probability …
Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice
R Fukushima, N Ueki - Annales Henri Poincaré, 2010 - Springer
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 …
the infimum of the spectrum is investigated. The leading term is determined when the decay …
Lifshitz tails for a class of Schrödinger operators with random breather-type potential
W Kirsch, I Veselić - Letters in Mathematical Physics, 2010 - Springer
We derive bounds on the integrated density of states for a class of Schrödinger operators
with a random potential. The potential depends on a sequence of random variables, not …
with a random potential. The potential depends on a sequence of random variables, not …
Quenched tail estimate for the random walk in random scenery and in random layered conductance II
JD Deuschel, R Fukushima - 2020 - projecteuclid.org
This is a continuation of our earlier work [Stochastic Processes and their Applications, 129
(1), pp. 102–128, 2019] on the random walk in random scenery and in random layered …
(1), pp. 102–128, 2019] on the random walk in random scenery and in random layered …
Low energy properties of the random displacement model
We study low-energy properties of the random displacement model, a random Schrödinger
operator describing an electron in a randomly deformed lattice. All periodic displacement …
operator describing an electron in a randomly deformed lattice. All periodic displacement …
Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential
R Fukushima, N Ueki - Journal of Functional Analysis, 2011 - Elsevier
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 …
potential around a randomly perturbed lattice is studied. The moment asymptotics of the total …
The parabolic Anderson model
W König, T Wolff - Preprint. Available at www. wiasberlin. de/people …, 2015 - Springer
This is a survey of the parabolic Anderson model (PAM), the Cauchy problem for the heat
equation with random potential. This model and many variants and related models are …
equation with random potential. This model and many variants and related models are …
[PDF][PDF] Classical behavior of the integrated density of states for the uniform magnetic field and a randomly perturbed lattice
N Ueki - Markov Process. Related Fields, 2011 - math.h.kyoto-u.ac.jp
For the Schrödinger operators on L2 (R2) and L2 (R3) with the uniform magnetic field and
the scalar potentials located at all sites of a randomly perturbed lattice, the asymptotic …
the scalar potentials located at all sites of a randomly perturbed lattice, the asymptotic …
Stochastic analysis and random Schrödinger operators
N Ueki - Sugaku Expositions, 2018 - ams.org
The Donsker-Varadhan theory on large deviations [12] and the Malliavin calculus [43] are
the main theories in the stochastic analysis founded in the latter twentieth century. Among …
the main theories in the stochastic analysis founded in the latter twentieth century. Among …