We give a new proof of Dixon's conjecture: The probability that a pair of random permutations generates either $A_n$ or $S_n$ is $1-1/n+\mathcal {O}(n^{-\frac{3}{2}+\epsilon})$. Our proof is based on character theory and character estimates and does not need the classification of the finite simple groups.
On the diameters of McKay graphs for finite simple groups
Towards the Classification of Finite Simple Groups with exactly Three or Four Supercharacter Theories
New Beauville surfaces and finite simple groups
![QR code for arXiv:1611.02501 [math.GR]](http://oss.arxitics.com/images/favicon.svg)