A finite group is -quasirandom if every nontrivial irreducible representation over the complex numbers has degree at least . The trivial representation is excluded. Large suppresses correlations of products of arbitrary subsets, through product mixing in a quasirandom group.
For an -quasirandom group, uniform expectations, and the normalized convolution on a finite group, a scalar mean-zero function satisfiesThe Fourier analysis on a finite group proof bounds each nontrivial matrix component of in operator norm using its weighted Hilbert-Schmidt norm. For subsets of subset density values , the error in their normalized product count is at most . In particular guarantees a solution of in the three subsets.
Articles by others on the same topic
A **quasirandom group** is a concept from group theory and representation theory, primarily relating to the properties of groups that exhibit a form of "randomness" in their structure. While the exact definition can vary depending on the context, quasirandom groups generally exhibit characteristics similar to random objects in a probabilistic sense. ### Key Features of Quasirandom Groups: 1. **Representations**: Quasirandom groups often have a large number of 'non-trivial' representations.