 
Summary: Approximating Probability Distributions Using
Small Sample Spaces
Yossi Azar \Lambda
Computer Science Department
Tel Aviv University
Tel Aviv 69978, Israel
Rajeev Motwani y
Computer Science Department
Stanford University
Stanford, CA 943052140
Joseph (Seffi) Naor z
Computer Science Department
Technion
Haifa 32000, Israel
Abstract
We formulate the notion of a ``good approximation'' to a probability distribution
over a finite abelian group G . The quality of the approximating distribution is char
acterized by a parameter ffl which is a bound on the difference between corresponding
Fourier coefficients of the two distributions. It is also required that the sample space
of the approximating distribution be of size polynomial in log jGj and 1=ffl. Such ap
