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