A disperser is a one-sided extractor.^[1] 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 ${\displaystyle A\subseteq \{0,1\}^{m}}$ we have: ${\displaystyle Pr_{U_{m}}[A]>1-\epsilon }$

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article needs additional citations for verification. (August 2012) This article may be too technical for most readers to understand. (January 2014)

Definition (Disperser): A ${\displaystyle (k,\epsilon )}$-disperser is a function

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

such that for every distribution ${\displaystyle X}$ on ${\displaystyle \{0,1\}^{n}}$ with ${\displaystyle H_{\infty }(X)\geq k}$ the support of the distribution ${\displaystyle Dis(X,U_{d})}$ is of size at least ${\displaystyle (1-\epsilon )2^{m}}$.

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.

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

• Expander graph