Asymptotic behaviour for critical slowing-down random walks

Details Asymptotic behaviour for critical slowing-down random walks Asymptotic behaviour for critical slowing-down random walks

2000-12-21

arxiv.org/abs/cond-mat/0012411v1

J. Stat. Phys. 101 (2000) 397-404

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures Brussels 1999 (G. Nicolis festschrift) invited talk

Scientific paper

The jump processes W(t) on [0,\infty[ with transitions w -> alpha w at rate
b*w^beta (0 =< alpha =< 1, b>0, beta>0) are considered. Their moments are shown
to decay not faster than algebraically for t -> \infty, and an equilibrium
probability density is found for a rescaled process U = (t + k)^{-beta} W. A
corresponding birth process is discussed.

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