Non-Gaussian fluctuations in stochastic models with absorbing barriers

Details Non-Gaussian fluctuations in stochastic models with absorbing barriers Non-Gaussian fluctuations in stochastic models with absorbing barriers

2011-04-29

arxiv.org/abs/1104.5570v1

Physics

Condensed Matter

Statistical Mechanics

2 figures, submitted to Phys. Rev. Lett

Scientific paper

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order corrections beyond the conventional Gaussian approximation. The theory is shown to successfully capture the non Gaussian traits of the sought distribution returning an excellent agreement with the simulations, for {\it all times} and arbitrarily {\it close} to the absorbing barrier. At large times, a compact analytical solution for the distribution of fluctuations is also obtained, bridging the gap with previous investigations, within the van Kampen picture and without resorting to alternative strategies, as elsewhere hypothesized.

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