Observation of light filaments induced in air by visible picosecond laser pulses

We report the observation of light filaments produced by a picosecond laser pulse in the visible. The pulse trapped in the filamentary mode experiences large-scale self-phase modulation, with almost 100-fold spectral broadening along with apparent shortening of the leading edge. Spatial-temporal properties of the light filament reveal rather complex propagation dynamics. Received: 7 August 2002 / Revised version: 12 September 2002 / Published online: 11 December 2002 RID="*" ID="*"Corresponding author. Fax: +370-2/3660-06, E-mail: audrius.dubietis@ff.vu.lt     

Large Deviations for the Markov Binomial Distribution

Considering the Markov binomial distribution, we study large deviations for the Poisson approximation. Apart from the standard choice of parameters, we use the approach where the parameter of approximation depends on the argument of the approximated distribution function.     

Local Theorems for the Markov Binomial Distribution

Considering the Markov binomial distribution, we study the accuracy of infinitely divisible approximations. A local version of the Kolmogorov first uniform theorem is obtained. Possible approximations in total variation are discussed.