7,782 research outputs found
Continuous time `true' self-avoiding random walk on Z
We consider the continuous time version of the `true' or `myopic'
self-avoiding random walk with site repulsion in 1d. The Ray-Knight-type method
which was applied to the discrete time and edge repulsion case, is applicable
to this model with some modifications. We present a limit theorem for the local
time of the walk and a local limit theorem for the displacement.Comment: 17 page
Existence and static stability of a capillary free surface appearing in a dewetted Bridgman process. I
This paper present six theoretical results concerning the existence and
static stability of a capillary free surface appearing in a dewetted Bridgman
crystal growth technique. The results are obtained in an axis symmetric 2D
model for semiconductors for which the sum of wetting angle and growth angle is
less than 180. Numerical results are presented in case of InSb semiconductor
growth. The reported results can help, the practical crystal growers, in better
understanding the dependence of the free surface shape and size on the pressure
difference across the free surface and prepare the appropriate seed size, and
thermal conditions before seeding the growth process.Comment: This is an extended version of the conference paper TIM 19 of 10pages
and 9 figure
Relaxed sector condition
In this note we present a new sufficient condition which guarantees
martingale approximation and central limit theorem a la Kipnis-Varadhan to hold
for additive functionals of Markov processes. This condition which we call the
relaxed sector condition (RSC) generalizes the strong sector condition (SSC)
and the graded sector condition (GSC) in the case when the self-adjoint part of
the infinitesimal generator acts diagonally in the grading. The main advantage
being that the proof of the GSC in this case is more transparent and less
computational than in the original versions. We also hope that the RSC may have
direct applications where the earlier sector conditions don't apply. So far we
don't have convincing examples in this direction.Comment: 11 page
On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh-gas
We consider the M -> 0 limit for tagged particle diffusion in a 1-dimensional
Rayleigh-gas, studied originaly by Sinai and Soloveichik (1986), respectively
by Szasz and Toth (1986). In this limit we derive a new type of model for
tagged paricle diffusion, with Calogero-Moser-Sutherland (i.e. inverse
quadratic) interaction potential between the two central particles. Computer
simulations on this new model reproduce exactly the numerical value of the
limiting variance obtained by Boldrighini, Frigio and Tognetti (2002).Comment: Dedicated to Domokos Szasz on his 65th birthda
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