Disperser

A disperser is a one-sided extractor. Where an extractor requires that every event gets the same probability under the uniform distribution and the extracted distribution, only the latter is required for a disperser. So for a disperser, an event $A\subseteq \{0,1{\}}^m$ we have: $P{r}_{U_m}[A]>1-ϵ$

Definition (Disperser): A $(k,ϵ)$-disperser is a function

$Dis:\{0,1{\}}^n\times \{0,1{\}}^d\to \{0,1{\}}^m$

such that for every distribution $X$ on $\{0,1{\}}^n$ with $H_{\mathrm{\infty }}(X)\ge k$ the support of the distribution $Dis(X,U_d)$ is of size at least $(1-ϵ)2^m$.

Graph theory

An (N, M, D, K, e)-disperser is a bipartite graph with N vertices on the left side, each with degree D, and M vertices on the right side, such that every subset of K vertices on the left side is connected to more than (1 − e)M vertices on the right.

An extractor is a related type of graph that guarantees an even stronger property; every (N, M, D, K, e)-extractor is also an (N, M, D, K, e)-disperser.

Other meanings

A disperser is a high-speed mixing device used to disperse or dissolve pigments and other solids into a liquid.

See also

• Expander graph

References

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