Disperser
A disperser is a one-sided extractor.<ref>Template:Cite journal</ref> 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 <math>A \subseteq \{0,1\}^{m}</math> we have: <math>Pr_{U_{m}}[A] > 1 - \epsilon</math>
Definition (Disperser): A <math>(k, \epsilon)</math>-disperser is a function
<math>Dis: \{0,1\}^{n}\times \{0,1\}^{d}\rightarrow \{0,1\}^{m}</math>
such that for every distribution <math>X</math> on <math>\{0,1\}^{n}</math> with <math>H_{\infty}(X) \geq k</math> the support of the distribution <math>Dis(X,U_{d})</math> is of size at least <math>(1-\epsilon)2^{m}</math>.
Graph theoryEdit
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 meaningsEdit
A disperser is a high-speed mixing device used to disperse or dissolve pigments and other solids into a liquid.