A universality class in Markovian persistence

Details A universality class in Markovian persistence A universality class in Markovian persistence

2000-04-10

arxiv.org/abs/cond-mat/0004147v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, LaTex

Scientific paper

10.1088/0305-4470/33/40/301

We consider the class of Markovian processes defined by the equation $\dd x /\dd t = -\beta x + \sum_k z_k \delta (t-t_k)$. Such processes are encountered in systems (like coalescing systems) where dynamics creates discrete upward jumps at random instants $t_k$ and of random height $z_k$. We observe that the probability for these processes to remain above their mean value during an interval of time $T$ decays as $\exp{-\theta T}$ defining $\theta$ as the persistence exponent. We show that $\theta$ takes the value $\beta$ which thereby extends the well known result of the Gaussian noise case to a much larger class of non-Gaussian processes.

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