Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

Diffusion approximation for equilibrium Kawasaki dynamics in continuum

A Kawasaki dynamics in continuum is a dynamics of an infinite system of interacting particles in $\mathbb R^d$ which randomly hop over the space. In this paper, we deal with an equilibrium Kawasaki dynamics which has a Gibbs measure $\mu$ as invariant measure. We study a diffusive limit of such a dynamics, derived through a scaling of both the jump rate and time. Under weak assumptions on the potential of pair interaction, $\phi$, (in particular, admitting a singularity of $\phi$ at zero), we prove that, on a set of smooth local functions, the generator of the scaled dynamics converges to the generator of the gradient stochastic dynamics. If the set on which the generators converge is a core for the diffusion generator, the latter result implies the weak convergence of finite-dimensional distributions of the corresponding equilibrium processes. In particular, if the potential $\phi$ is from $C_{\mathrm b}^3(\mathbb R^d)$ and sufficiently quickly converges to zero at infinity, we conclude the convergence of the processes from a result in [Choi {\it et al.}, J. Math. Phys. 39 (1998) 6509--6536]

Review of overall parameters of giant radio pulses from the Crab pulsar and B1937+21

We present a review of observed parameters of giant radio pulses, based on the observations conducted by our group during recent years. The observations cover a broad frequency range of about 3 octaves, concentrating between 600 and 4850 MHz. Giant pulses of both the Crab pulsar and the millisecond pulsar B1937+21 were studied with the 70-m Tidbinbilla, the 100-m GBT, 64-m Kalyazin and Westerbork radio telescopes. We discuss pulse energy distribution, dependence of peak flux density from the pulse width, peculiarities of radio spectra, and polarization properties of giant radio pulses.Comment: 3 pages, 4 figures, to be published in the Proceedings of the conference "40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More" held on August 12-17, 2007, McGill University, Montreal, Canad