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I am reading the paper "A statistical theory of continuous double auction". The paper can be found at,

https://www.santafe.edu/research/results/working-papers/statistical-theory-of-the-continuous-double-auctio

On page 20, section F-3 titled "Screening of the market-order rate", the author states as follows. I am trying to undestand how the relationship $d\mu = -\mu (1-\pi_0)$ is arrived at. Here $\pi_0$ is the probability of zero occupation at site with price $p$. I would imagine that this is a fairly known result in physics, or physical chemistry. I would imagine there is probably a result in eletrostatic screening or diffusion problems in the presense of barriers.

I was hoping someone could point me to references or introductory exposition of anything related to this derivation.

Thank you,

  1. Screening of the market-order rate

In the context of independent fluctuations, Eq. (26) implies a relation between the mean density and the rate at which market orders are screened as price increases. The effect of a limit order, resident in the price bin p when a market order survives to reach that bin, is to prevent its arriving at the bin at p + dp. Though the nature of the shift induced, when such annihilation occurs, depends 21 on the comoving frame being modeled, the change in the number of orders surviving is independent of frame, and is given by $\mu = - \mu (1 - \pi_0) = -\frac{\mu <n>}{\sigma}$. (29)

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